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

0,7

Comments

Subsequence of A007318.

Links

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

Formula

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

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

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

Example

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

Mathematica

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

Prog

(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] ; )

Crossrefs

Cf. A000045, A007318.

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

Sequence in context: A034364 A183610 A261365 * A304942 A090011 A061554

Adjacent sequences: A261504 A261505 A261506 * A261508 A261509 A261510

Keyword

less,nonn,tabf

Author

Maghraoui Abdelkader, Aug 22 2015

Status

approved