A261507 Fibonacci-numbered rows of Pascal's triangle. Triangle read by rows: T(n,k)= binomial(Fibonacci(n), k).

1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 5, 10, 10, 5, 1, 1, 8, 28, 56, 70, 56, 28, 8, 1, 1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1, 1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490, 293930, 352716, 352716, 293930, 203490, 116280, 54264, 20349, 5985, 1330, 210, 21, 1

Offset: 0

Author

Maghraoui Abdelkader, Aug 22 2015

Keywords

• less
• nonn
• tabf

Comments

Subsequence of A007318.

Examples

			1,
1,  1,
1,  1,
1,  2,  1,
1,  3,  3,   1,
1,  5, 10,  10,   5,    1,
1,  8, 28,  56,  70,   56,   28,    8,    1,
1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1
		

Links

• Jean-François Alcover, Table of n, a(n) for n = 0..388 (corrected by _N. J. A. Sloane_, Jan 18 2019)

Crossrefs

Cf. A000045, A007318.

Cf. A036355, A037027, A228074, A162741, A034871, A034870, A191797.

Programs

Mathematica

Table[Binomial[Fibonacci[n], k], {n, 0, 8}, {k, 0, Fibonacci[n]}]//Flatten (* Jean-François Alcover, Nov 12 2015*)

PARI

v = vector(101,j,fibonacci(j)); i=0; n=0; while(n<100, for(k=0, n, print1(binomial(n, k), ", ","")); print(); i=i+1; n=v[i] ;)

Formula

T(n, k) = binomial(fibonacci(n), k).

T(n, 1) = fibonacci(n) = A000045(n).

T(n, 2) = A191797(n) for n>3.