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

0,4

Links

Table of n, a(n) for n=0..65.

Formula

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).

Example

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

Crossrefs

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

Sequence in context: A119348 A282935 A354223 * A322589 A185312 A185311

Adjacent sequences: A181971 A181972 A181973 * A181975 A181976 A181977

Keyword

easy,nonn,tabl

Author

Philippe Deléham, Apr 06 2012

Status

approved