A162745 A Fibonacci-Pascal triangle.

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

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: A362242 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