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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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: A030306 A119348 A282935 * A322589 A185312 A185311

Adjacent sequences:  A181971 A181972 A181973 * A181975 A181976 A181977

KEYWORD

easy,nonn,tabl

AUTHOR

Philippe Deléham, Apr 06 2012

STATUS

approved

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Last modified March 2 08:39 EST 2021. Contains 341745 sequences. (Running on oeis4.)