A103577 Number of partitions of n into Fibonacci parts if each part is of two kinds.

1, 2, 5, 10, 18, 32, 53, 84, 132, 198, 294, 426, 606, 852, 1178, 1610, 2178, 2910, 3859, 5066, 6598, 8534, 10951, 13968, 17705, 22304, 27959, 34852, 43239, 53402, 65649, 80384, 98025, 119078, 144149, 173866, 209033, 250510, 299283, 356532, 423508

Offset

0,2

Comments

Euler transform of 2 x the characteristic function of the Fibonacci numbers.

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

G.f.=1/product((1-x^fibonacci(i))^2, i=2..infinity).

Example

a(3)=10 because we have 3, 3', 2+1, 2+1', 2'+1, 2'+1', 1+1+1, 1+1+1', 1+1'+1' and 1'+1'+1'.

Maple

N:= 12: # to get a(0)..a(M-1) where M = Fibonacci(N-1).
G:= mul(1/(1-x^combinat:-fibonacci(i))^2, i=2..N-1):
S:= series(G, x, combinat:-fibonacci(N)):
seq(coeff(S, x, j), j=0..combinat:-fibonacci(N)-1); # Robert Israel, Dec 01 2017

Crossrefs

Cf. A003107, A000045.

Sequence in context: A006327 A185721 A304796 * A326508 A079006 A001936

Adjacent sequences: A103574 A103575 A103576 * A103578 A103579 A103580

Keyword

nonn

Author

Emeric Deutsch, Mar 23 2005

Status

approved