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A162745 A Fibonacci-Pascal triangle. 1
1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 20, 10, 1, 1, 15, 50, 50, 15, 1, 1, 21, 105, 173, 105, 21, 1, 1, 28, 196, 476, 476, 196, 28, 1, 1, 36, 336, 1120, 1643, 1120, 336, 36, 1, 1, 45, 540, 2352, 4707, 4707, 2352, 540, 45, 1, 1, 55, 825, 4530, 11775, 16040, 11775, 4530, 825, 55, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are A162746.

LINKS

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

Paul Barry, On a Generalization of the Narayana Triangle, J. Int. Seq. 14 (2011) # 11.4.5.

FORMULA

T(n,k) = Sum_{j=0..n} C(n,j)*C(n-j,2(k-j))*Fibonacci(k-j+1).

EXAMPLE

Triangle begins

1;

1, 1;

1, 3, 1;

1, 6, 6, 1;

1, 10, 20, 10, 1;

1, 15, 50, 50, 15, 1;

1, 21, 105, 173, 105, 21, 1;

1, 28, 196, 476, 476, 196, 28, 1;

1, 36, 336, 1120, 1643, 1120, 336, 36, 1;

1, 45, 540, 2352, 4707, 4707, 2352, 540, 45, 1;

PROG

(PARI) T(n, k)=sum(j=0, n, binomial(n, j)*binomial(n-j, 2*(k-j))*fibonacci(k-j+1));

row(n) = vector(n+1, k, T(n, k-1)); \\ Michel Marcus, Nov 11 2022

CROSSREFS

Cf. A000045.

Sequence in context: A299146 A114176 A056241 * A001263 A162747 A107105

Adjacent sequences: A162742 A162743 A162744 * A162746 A162747 A162748

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Jul 12 2009

STATUS

approved

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Last modified December 5 15:27 EST 2022. Contains 358588 sequences. (Running on oeis4.)