Sequences

392,541 sequences

a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 - a(k)^2 for 1<=i<j<k<=n.A026511
a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 - a(k)^2 for 1<=i<j<k<=n.
a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 - a(k)^2 for 1<=i<=j<=k<=n.A026512
a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 - a(k)^2 for 1<=i<=j<=k<=n.
a(n) = t(2+3n), where t = A001285 (Thue-Morse sequence).A026513
a(n) = t(2+3n), where t = A001285 (Thue-Morse sequence).
a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 + a(k)^2 for 1<=i<=j<=k<=n.A026514
a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 + a(k)^2 for 1<=i<=j<=k<=n.
a(n) = length of n-th run of identical symbols in A026513.A026515
a(n) = length of n-th run of identical symbols in A026513.
a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 + a(k)^2 for 1<=i<=j<=k<=n.A026516
a(n) = least positive integer > a(n-1) and not (a(i)+a(j))^2 + a(k)^2 for 1<=i<=j<=k<=n.
a(n) = t(5n), where t = A001285 (Thue-Morse sequence).A026517
a(n) = t(5n), where t = A001285 (Thue-Morse sequence).
a(n) = length of n-th run of identical symbols in A026517.A026518
a(n) = length of n-th run of identical symbols in A026517.
Irregular triangular array T read by rows: T(n, k) = T(n-1, k-2) + T(n-1, k) if (n mod 2) = 0, otherwise T(n-1, k-2) + T(n-1, k-1) + T(n-1, k), with T(n, 0) = T(n, 2*n) = 1, T(n, 1) = T(n, 2*n-1) = floor((n+1)/2).A026519
Irregular triangular array T read by rows: T(n, k) = T(n-1, k-2) + T(n-1, k) if (n mod 2) = 0, otherwise T(n-1, k-2) + T(n-1, k-1) + T(n-1, k), with T(n, 0) = T(n, 2*n) = 1, T(n, 1) = T(n, 2*n-1) = floor((n+1)/2).
a(n) = T(n,n), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 0.A026520
a(n) = T(n,n), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 0.
a(n) = T(n, n-1), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.A026521
a(n) = T(n, n-1), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.
a(n) = T(n, n-2), where T is given by A026519. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.A026522
a(n) = T(n, n-2), where T is given by A026519. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.
a(n) = T(n, n-3), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 3.A026523
a(n) = T(n, n-3), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 3.
a(n) = T(n, n-4), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 4.A026524
a(n) = T(n, n-4), T given by A026519. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 4.
a(n) = T(2*n, n), where T is given by A026519.A026525
a(n) = T(2*n, n), where T is given by A026519.
a(n) = T(2n,n-1), T given by A026519.A026526
a(n) = T(2n,n-1), T given by A026519.
a(n) = T(2*n, n-2), where T is given by A026519.A026527
a(n) = T(2*n, n-2), where T is given by A026519.
a(n) = T(2*n-1, n-1), T given by A026519.A026528
a(n) = T(2*n-1, n-1), T given by A026519.
a(n) = T(2*n-1, n-2), where T is given by A026519.A026529
a(n) = T(2*n-1, n-2), where T is given by A026519.
a(n) = T(n, floor(n/2)), T given by A026519.A026530
a(n) = T(n, floor(n/2)), T given by A026519.
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026519.A026531
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026519.
Ratios of successive terms are 3, 2, 3, 2, 3, 2, 3, 2, ...A026532
Ratios of successive terms are 3, 2, 3, 2, 3, 2, 3, 2, ...
a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026519.A026533
a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026519.
a(n) = Sum_{i=0..2*n} Sum_{j=0..n-1} A026519(j, i).A026534
a(n) = Sum_{i=0..2*n} Sum_{j=0..n-1} A026519(j, i).
a(n) = t(1+5n) where t = A001285 (Thue-Morse sequence).A026535
a(n) = t(1+5n) where t = A001285 (Thue-Morse sequence).
Irregular triangular array T read by rows: T(i,0 ) = T(i,2i) = 1 for i >= 0; T(i,1) = T(i,2i-1) = floor(i/2) for i >= 1; for even n >= 2, T(i,j) = T(i-1,j-2) + T(i-1,j-1) + T(i-1,j) for j = 2..2i-2, for odd n >= 3, T(i,j) = T(i-1,j-2) + T(i-1,j) for j = 2..2i-2.A026536
Irregular triangular array T read by rows: T(i,0 ) = T(i,2i) = 1 for i >= 0; T(i,1) = T(i,2i-1) = floor(i/2) for i >= 1; for even n >= 2, T(i,j) = T(i-1,j-2) + T(i-1,j-1) + T(i-1,j) for j = 2..2i-2, for odd n >= 3, T(i,j) = T(i-1,j-2) + T(i-1,j) for j = 2..2i-2.
a(n) = T(n,n), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n)=0.A026537
a(n) = T(n,n), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n)=0.
a(n) = T(n,n-1), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.A026538
a(n) = T(n,n-1), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 1.
a(n) = T(n,n-2), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.A026539
a(n) = T(n,n-2), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 2.
a(n) = T(n,n-3), T given by A026536. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 3.A026540
a(n) = T(n,n-3), T given by A026536. Also number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 3.
a(n) = T(n,n-4), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 4.A026541
a(n) = T(n,n-4), T given by A026536. Also a(n) = number of integer strings s(0), ..., s(n), counted by T, such that s(n) = 4.
Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)*(1-11*x)).A026542
Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)*(1-11*x)).
Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)*(1-12*x)).A026543
Expansion of 1/((1-2*x)*(1-6*x)*(1-7*x)*(1-12*x)).
Duplicate of A026527.A026544
Duplicate of A026527.
a(n) = T(2n-1, n-1), T given by A026536.A026545
a(n) = T(2n-1, n-1), T given by A026536.
a(n) = T(2n-1,n-2), T given by A026536.A026546
a(n) = T(2n-1,n-2), T given by A026536.
a(n) = T(n, floor(n/2)), T given by A026536.A026547
a(n) = T(n, floor(n/2)), T given by A026536.
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026536.A026548
a(n) = T(n,0) + T(n,1) + ... + T(n,n), T given by A026536.
Ratios of successive terms are 2, 3, 2, 3, 2, 3, 2, 3, ...A026549
Ratios of successive terms are 2, 3, 2, 3, 2, 3, 2, 3, ...
a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026536.A026550
a(n) = Sum_{i=0..n} Sum_{j=0..i} T(i,j), T given by A026536.
Expansion of 3*(1+2*x-2*x^2)/((1-x)*(1-6*x^2)).A026551
Expansion of 3*(1+2*x-2*x^2)/((1-x)*(1-6*x^2)).
Irregular triangular array T read by rows: T(n, 0) = T(n, 2*n) = 1, T(n, 1) = T(n, 2*n-1) = floor(n/2 + 1), for even n >= 2, T(n, k) = T(n-1, k-2) + T(n-1, k-1) + T(n-1, k), otherwise T(n, k) = T(n-1, k-2) + T(n-1, k).A026552
Irregular triangular array T read by rows: T(n, 0) = T(n, 2*n) = 1, T(n, 1) = T(n, 2*n-1) = floor(n/2 + 1), for even n >= 2, T(n, k) = T(n-1, k-2) + T(n-1, k-1) + T(n-1, k), otherwise T(n, k) = T(n-1, k-2) + T(n-1, k).
a(n) = T(n,n), T given by A026552. Also a(n) is the number of integer strings s(0),...,s(n) counted by T, such that s(n)=0.A026553
a(n) = T(n,n), T given by A026552. Also a(n) is the number of integer strings s(0),...,s(n) counted by T, such that s(n)=0.
a(n) = T(n,n-1), T given by A026552. Also a(n) is the number of integer strings s(0),...,s(n) counted by T, such that s(n)=1.A026554
a(n) = T(n,n-1), T given by A026552. Also a(n) is the number of integer strings s(0),...,s(n) counted by T, such that s(n)=1.
a(n) = T(n, n-2), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 2.A026555
a(n) = T(n, n-2), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 2.
a(n) = T(n, n-3), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 3.A026556
a(n) = T(n, n-3), T given by A026552. Also a(n) = number of integer strings s(0), ..., s(n) counted by T, such that s(n) = 3.
a(n) = T(n, n-4), T given by A026552. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4.A026557
a(n) = T(n, n-4), T given by A026552. Also a(n) = number of integer strings s(0),...,s(n) counted by T, such that s(n)=4.
a(n) = T(2*n, n), where T is given by A026552.A026558
a(n) = T(2*n, n), where T is given by A026552.
a(n) = T(2*n, n-1), where T is given by A026552.A026559
a(n) = T(2*n, n-1), where T is given by A026552.
a(n) = T(2*n, n-2), where T is given by A026552.A026560
a(n) = T(2*n, n-2), where T is given by A026552.