Sequences

392,541 sequences

a(n) = A027052(n, 2n-5).A027061
a(n) = A027052(n, 2n-5).
a(n) = A027052(n, 2n-6).A027062
a(n) = A027052(n, 2n-6).
a(n) = A027052(n, 2n-7).A027063
a(n) = A027052(n, 2n-7).
a(n) = A027052(n, 2n-8).A027064
a(n) = A027052(n, 2n-8).
a(n) = A027052(n, 2n-9).A027065
a(n) = A027052(n, 2n-9).
a(n) = A027052(n, 2n-10).A027066
a(n) = A027052(n, 2n-10).
a(n) = Sum_{k=n..2*n} T(n,k), T given by A027052.A027067
a(n) = Sum_{k=n..2*n} T(n,k), T given by A027052.
a(n) = Sum_{i=0..n} Sum_{j=i..2*i} A027052(i, j).A027068
a(n) = Sum_{i=0..n} Sum_{j=i..2*i} A027052(i, j).
a(n) = diagonal sum of left-justified array T given by A027052.A027069
a(n) = diagonal sum of left-justified array T given by A027052.
a(n) = diagonal sum of right-justified array T given by A027052.A027070
a(n) = diagonal sum of right-justified array T given by A027052.
Greatest number in row n of array T given by A027052.A027071
Greatest number in row n of array T given by A027052.
a(n) = self-convolution of row n of array T given by A027052.A027072
a(n) = self-convolution of row n of array T given by A027052.
a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027052.A027073
a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027052.
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027052.A027074
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027052.
a(n) = Sum_{k=0..2n} (k+1) * A027052(n, k).A027075
a(n) = Sum_{k=0..2n} (k+1) * A027052(n, k).
a(n) = Sum_{k=0..2n} (k+1) * A027052(n, 2n-k).A027076
a(n) = Sum_{k=0..2n} (k+1) * A027052(n, 2n-k).
a(n) = Sum_{k=n+1..2*n} T(n,k), T given by A027052.A027077
a(n) = Sum_{k=n+1..2*n} T(n,k), T given by A027052.
a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027052.A027078
a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027052.
a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027052.A027079
a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027052.
a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027052.A027080
a(n) = Sum_{k=0..2n-2} T(n,k) * T(n,k+2), with T given by A027052.
a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027052.A027081
a(n) = Sum_{k=0..2n-3} T(n,k) * T(n,k+3), with T given by A027052.
Irregular triangular array: T(n,0) = 1 for n >= 1; T(n,1) = T(n,2) = 1 for n >= 1; T(n,k) = T(n-1,k-3) + T(n-1,k-2) + T(n-1,k-1) for 3 <= k <= 2n-1 and n >= 2; and T(n,2n) = T(n-1,2n-3) + T(n-1,2n-2) for n >= 2.A027082
Irregular triangular array: T(n,0) = 1 for n >= 1; T(n,1) = T(n,2) = 1 for n >= 1; T(n,k) = T(n-1,k-3) + T(n-1,k-2) + T(n-1,k-1) for 3 <= k <= 2n-1 and n >= 2; and T(n,2n) = T(n-1,2n-3) + T(n-1,2n-2) for n >= 2.
a(n) = A027082(n, n+2).A027083
a(n) = A027082(n, n+2).
G.f.: x^2*(x^2 + x + 1)/(x^4 - 2*x + 1).A027084
G.f.: x^2*(x^2 + x + 1)/(x^4 - 2*x + 1).
a(n) = A027082(n, n+3).A027085
a(n) = A027082(n, n+3).
a(n) = A027082(n, n+4).A027086
a(n) = A027082(n, n+4).
a(n) = A027082(n, 2n).A027087
a(n) = A027082(n, 2n).
a(n) = A027082(n, 2n-1).A027088
a(n) = A027082(n, 2n-1).
a(n) = A027082(n, 2n-2).A027089
a(n) = A027082(n, 2n-2).
a(n) = A027082(n, 2n-3).A027090
a(n) = A027082(n, 2n-3).
a(n) = A027082(n, 2n-4).A027091
a(n) = A027082(n, 2n-4).
a(n) = A027082(n, 2n-5).A027092
a(n) = A027082(n, 2n-5).
a(n) = A027082(n, 2n-6).A027093
a(n) = A027082(n, 2n-6).
a(n) = A027082(n, 2n-7).A027094
a(n) = A027082(n, 2n-7).
a(n) = A027082(n, 2n-8).A027095
a(n) = A027082(n, 2n-8).
a(n) = A027082(n, 2n-9).A027096
a(n) = A027082(n, 2n-9).
a(n) = A027082(n, 2n-10).A027097
a(n) = A027082(n, 2n-10).
T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027082.A027098
T(n,n) + T(n,n+1) + ... + T(n,2n), T given by A027082.
a(n) = Sum_{0<=i<=i<=n} A027082(i, n+j).A027099
a(n) = Sum_{0<=i<=i<=n} A027082(i, n+j).
Diagonal sum of left justified array T given by A027082.A027100
Diagonal sum of left justified array T given by A027082.
a(n) = diagonal sum of right justified array T given by A027082.A027101
a(n) = diagonal sum of right justified array T given by A027082.
a(n) = greatest number in row n of array T given by A027082.A027102
a(n) = greatest number in row n of array T given by A027082.
a(n) = self-convolution of row n of array T given by A027082.A027103
a(n) = self-convolution of row n of array T given by A027082.
a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027082.A027104
a(n) = Sum_{k=0..n} T(n,k) * T(n,2n-k), with T given by A027082.
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027082.A027105
a(n) = Sum_{k=0..n-1} T(n,k) * T(n,2n-k), with T given by A027082.
a(n) = Sum_{k=0..2n} (k+1) * A027082(n, k).A027106
a(n) = Sum_{k=0..2n} (k+1) * A027082(n, k).
a(n) = Sum_{k=0..2n} (k+1) * A027082(n, 2n-k).A027107
a(n) = Sum_{k=0..2n} (k+1) * A027082(n, 2n-k).
a(n) = T(n,n+1) + T(n,n+2) + ... + T(n,2n), T given by A027082.A027108
a(n) = T(n,n+1) + T(n,n+2) + ... + T(n,2n), T given by A027082.
a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027082.A027109
a(n) = Sum_{k=0..n} T(n,k) * T(n,n+k), with T given by A027082.
a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027082.A027110
a(n) = Sum_{k=0..2n-1} T(n,k) * T(n,k+1), with T given by A027082.