A001872 -id:A001872 - cp's OEIS frontend

A181974 Triangle T(n,k), read by rows, given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

1, 1, 1, 2, 3, 1, 3, 4, 2, 1, 5, 7, 5, 4, 1, 8, 11, 10, 9, 3, 1, 13, 18, 20, 20, 9, 5, 1, 21, 29, 38, 40, 22, 15, 4, 1, 34, 47, 71, 78, 51, 40, 14, 6, 1, 55, 76, 130, 147, 111, 95, 40, 22, 5, 1, 89, 123, 235, 272, 233, 213, 105, 68, 20, 7, 1

Offset: 0

Philippe Deléham, Apr 06 2012

			Triangle begins :
1
1, 1
2, 3, 1
3, 4, 2, 1
5, 7, 5, 4, 1
8, 11, 10, 9, 3, 1
13, 18, 20, 20, 9, 5, 1
21, 29, 38, 40, 22, 15, 4, 1
34, 47, 71, 78, 51, 40, 14, 6, 1
55, 76, 130, 147, 111, 95, 40, 22, 5, 1
89, 123, 235, 272, 233, 213, 105, 68, 20, 7, 1
144, 199, 420, 495, 474, 455, 256, 185, 65, 30, 6, 1

Cf. Columns : A000045, A000032, A001629, A023607, A001628, A152881, A001872, A001873

G.f.: (1+y*x+2*y*x^2)/(1-x-x^2-y^2*x^2).
T(n,k) = T(n-1,k) + T(n-2,k) + T(n-2,k-2), T(0,0) = T(1,0) = T(1,1) = T(2,2) = 1, T(2,0) = 2, T(2,1) = 3 and T(n,k) = 0 if k<0 or if k>n.
T(n + 2k, 2k) = A037027(n + k, k).
T(n + 2k +1, 2k + 1) = A182001(n + k, k).
T(n,0) = Fibonacci(n+1).

cp's OEIS Frontend

A181974 Triangle T(n,k), read by rows, given by (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, -3, 2, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938.

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