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A161026 Number of partitions of n into Fibonacci numbers where every part appears at least 2 times. 1
1, 0, 1, 1, 2, 1, 4, 2, 5, 5, 8, 6, 12, 10, 15, 16, 22, 20, 30, 30, 38, 40, 51, 51, 67, 69, 84, 88, 108, 111, 136, 141, 168, 176, 209, 218, 256, 267, 310, 328, 376, 396, 454, 477, 541, 575, 644, 681, 767, 809, 902, 959, 1061, 1121, 1246, 1316, 1448, 1537, 1687, 1781, 1956 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (terms n=1..1000 from R. H. Hardin)

FORMULA

G.f.: Product(1+x^(2*F(j))/(1-x^(F(j))), j=2..infinity), where F = A000045 are the Fibonacci numbers. -  Emeric Deutsch, Jun 24 2009

EXAMPLE

a(9) = 5 because we have 333, 33111, 222111, 2211111, and 1^9. - Emeric Deutsch, Jun 24 2009

MAPLE

with(combinat); g := product(1+x^(2*fibonacci(j))/(1-x^fibonacci(j)), j = 2 .. 10): gser := series(g, x = 0, 95): seq(coeff(gser, x, n), n = 0 .. 65); # Emeric Deutsch, Jun 24 2009

# second Maple program:

F:= proc(n, i) option remember; (<<0|1>, <1|1>>^n)[1, 2] end:

b:= proc(n, i) option remember; `if`(n=0, 1, (f-> `if`(2*f<=n,

      add(b(n-j*f, i+1), j=[0, $2..n/f]), 0))(F(i)))

    end:

a:= n-> b(n, 2):

seq(a(n), n=0..80);  # Alois P. Heinz, Feb 23 2019

CROSSREFS

Cf. A000045.

Sequence in context: A128861 A161307 A161241 * A161077 A161293 A217916

Adjacent sequences:  A161023 A161024 A161025 * A161027 A161028 A161029

KEYWORD

nonn

AUTHOR

R. H. Hardin, Jun 02 2009

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Feb 23 2019

STATUS

approved

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Last modified July 15 22:48 EDT 2019. Contains 325061 sequences. (Running on oeis4.)