Sequences

392,541 sequences

a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A026703.A026711
a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A026703.
a(n) = Sum{T(i,j)}, 0<=i<=n, 0<=j<=n, T given by A026703.A026712
a(n) = Sum{T(i,j)}, 0<=i<=n, 0<=j<=n, T given by A026703.
Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A026703.A026713
Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A026703.
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if k=[ (n-1)/2 ] or k=[ n/2 ] or k=[ (n+2)/2 ], else T(n,k)=T(n-1,k-1)+T(n-1,k).A026714
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1<=k<=n-1, T(n,k)=T(n-1,k-1)+T(n-2,k-1)+T(n-1,k) if k=[ (n-1)/2 ] or k=[ n/2 ] or k=[ (n+2)/2 ], else T(n,k)=T(n-1,k-1)+T(n-1,k).
T(2n,n), T given by A026714.A026715
T(2n,n), T given by A026714.
T(2n,n-1), T given by A026714.A026716
T(2n,n-1), T given by A026714.
T(2n,n-2), T given by A026714.A026717
T(2n,n-2), T given by A026714.
T(2n-1,n-1), T given by A026714.A026718
T(2n-1,n-1), T given by A026714.
T(2n-1,n-2), T given by A026714.A026719
T(2n-1,n-2), T given by A026714.
T(n,[ n/2 ]), T given by A026714.A026720
T(n,[ n/2 ]), T given by A026714.
T(n,0) + T(n,1) + ... + T(n,n), T given by A026714.A026721
T(n,0) + T(n,1) + ... + T(n,n), T given by A026714.
a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A026714.A026722
a(n) = T(n,0) + T(n,1) + ... + T(n,[ n/2 ]), T given by A026714.
a(n) = Sum{T(i,j)}, 0<=i<=n, 0<=j<=i, T given by A026714.A026723
a(n) = Sum{T(i,j)}, 0<=i<=n, 0<=j<=i, T given by A026714.
Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A026714.A026724
Sum{T(n-k,k)}, 0<=k<=[ n/2 ], T given by A026714.
Triangular array, T, read by rows: T(n,0) = T(n,n) = 1. For n >= 2 and 1<=k<=n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is odd and k=n/2, otherwise T(n,k) = T(n-1,k-1) + T(n-1,k).A026725
Triangular array, T, read by rows: T(n,0) = T(n,n) = 1. For n >= 2 and 1<=k<=n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is odd and k=n/2, otherwise T(n,k) = T(n-1,k-1) + T(n-1,k).
a(n) = T(2n,n), T given by A026725.A026726
a(n) = T(2n,n), T given by A026725.
Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)*(1-11*x)).A026727
Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)*(1-11*x)).
a(n) = number of primes of the form k*(n-k) + 1.A026728
a(n) = number of primes of the form k*(n-k) + 1.
Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.A026729
Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.
a(8n)=n, a(8n+4)=a(8n)+a(8n+8), a(4n+2)=a(4n)+a(4n+4), a(2n+1)=a(2n)+a(2n+2).A026730
a(8n)=n, a(8n+4)=a(8n)+a(8n+8), a(4n+2)=a(4n)+a(4n+4), a(2n+1)=a(2n)+a(2n+2).
Greatest number in row n of array T given by A026725.A026731
Greatest number in row n of array T given by A026725.
a(n) = Sum_{k=0..n} T(n,k), T given by A026725.A026732
a(n) = Sum_{k=0..n} T(n,k), T given by A026725.
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026725.A026733
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026725.
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026725.A026734
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026725.
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026725.A026735
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026725.
Triangular array T read by rows: T(n,0) = T(n,n) = 1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is even and k=(n-2)/2, otherwise T(n,k) = T(n-1,k-1) + T(n-1,k).A026736
Triangular array T read by rows: T(n,0) = T(n,n) = 1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is even and k=(n-2)/2, otherwise T(n,k) = T(n-1,k-1) + T(n-1,k).
a(n) = T(2*n,n), T given by A026736.A026737
a(n) = T(2*n,n), T given by A026736.
Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)*(1-12*x)).A026738
Expansion of 1/((1-2*x)*(1-6*x)*(1-8*x)*(1-12*x)).
Number of subgroups L of Z^n with the property that for every a in Z^n there exists precisely one b in L with d(a,b) <= 1. Here d denotes Euclidean distance.A026739
Number of subgroups L of Z^n with the property that for every a in Z^n there exists precisely one b in L with d(a,b) <= 1. Here d denotes Euclidean distance.
a(n) = 2^n*(2^n - 1)*(2^n - 2)/6.A026740
a(n) = 2^n*(2^n - 1)*(2^n - 2)/6.
a(n) = n if n odd, n/2 if n even.A026741
a(n) = n if n odd, n/2 if n even.
a(n) = T(n, floor(n/2)), T given by A026736.A026742
a(n) = T(n, floor(n/2)), T given by A026736.
a(n) = Sum_{j=0..n} T(n,j), T given by A026736.A026743
a(n) = Sum_{j=0..n} T(n,j), T given by A026736.
a(n) = Sum_{j=0..floor(n/2)} T(n,j), T given by A026736.A026744
a(n) = Sum_{j=0..floor(n/2)} T(n,j), T given by A026736.
a(n) = Sum_{j=0..n} Sum_{i=0..n} T(j,i), T given by A026736.A026745
a(n) = Sum_{j=0..n} Sum_{i=0..n} T(j,i), T given by A026736.
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026736.A026746
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026736.
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is even and 1 <= k <= n/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).A026747
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is even and 1 <= k <= n/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).
a(n) = T(2n,n), T given by A026747.A026748
a(n) = T(2n,n), T given by A026747.
a(n) = T(2n,n-1), T given by A026747.A026749
a(n) = T(2n,n-1), T given by A026747.
a(n) = T(2n,n-2), T given by A026747.A026750
a(n) = T(2n,n-2), T given by A026747.
a(n) = T(2n-1,n-1), T given by A026747.A026751
a(n) = T(2n-1,n-1), T given by A026747.
a(n) = T(2n-1,n-2), T given by A026747.A026752
a(n) = T(2n-1,n-2), T given by A026747.
a(n) = T(n, floor(n/2)), T given by A026747.A026753
a(n) = T(n, floor(n/2)), T given by A026747.
a(n) = Sum{k=0..n} T(n,k), T given by A026747.A026754
a(n) = Sum{k=0..n} T(n,k), T given by A026747.
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026747.A026755
a(n) = Sum_{k=0..floor(n/2)} T(n,k), T given by A026747.
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026747.A026756
a(n) = Sum_{i=0..n} Sum_{j=0..n} T(i,j), T given by A026747.
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026747.A026757
a(n) = Sum_{k=0..floor(n/2)} T(n-k,k), T given by A026747.
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is odd and 1 <= k <= (n-1)/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).A026758
Triangular array T read by rows: T(n,0)=T(n,n)=1 for n >= 0; for n >= 2 and 1 <= k <= n-1, T(n,k) = T(n-1,k-1) + T(n-2,k-1) + T(n-1,k) if n is odd and 1 <= k <= (n-1)/2, else T(n,k) = T(n-1,k-1) + T(n-1,k).
a(n) = T(2n, n), T given by A026758.A026759
a(n) = T(2n, n), T given by A026758.
a(n) = T(2n, n-1), T given by A026758.A026760
a(n) = T(2n, n-1), T given by A026758.