login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A093997 Number of partitions of n with an odd number of distinct Fibonacci parts. 5
0, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 3, 1, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 1, 3, 2, 3, 2, 1, 3, 2, 2, 3, 1, 2, 3, 2, 3, 1, 2, 2, 0, 3, 2, 2, 3, 2, 3, 3, 2, 4, 2, 2, 4, 1, 3, 3, 2, 4, 2, 3, 3, 1, 3, 3, 3, 4, 1, 3, 3, 1, 4, 2, 2, 2, 1, 3, 2, 2, 4, 2, 3, 4, 2, 4, 3, 3, 5, 1, 4, 4, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10946

FORMULA

G.f.: (Product_{k>=2} (1 + x^{F_k}) - Product_{k>=2} (1 - x^{F_k}))/2.

MAPLE

F:= combinat[fibonacci]:

b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<2, 0,

       b(n, i-1, t)+`if`(F(i)>n, 0, b(n-F(i), i-1, 1-t))))

    end:

a:= proc(n) local j; for j from ilog[(1+sqrt(5))/2](n+1)

       while F(j+1)<=n do od; b(n, j, 0)

    end:

seq(a(n), n=0..100);  # Alois P. Heinz, Jul 11 2013

MATHEMATICA

Take[ CoefficientList[ Expand[ Product[1 + x^Fibonacci[k], {k, 2, 13}]/2 - Product[1 - x^Fibonacci[k], {k, 2, 13}]/2], x], 105] (* Robert G. Wilson v, May 29 2004 *)

CROSSREFS

Cf. A000119.

Sequence in context: A193348 A263723 A318498 * A157196 A300410 A293451

Adjacent sequences:  A093994 A093995 A093996 * A093998 A093999 A094000

KEYWORD

nonn,look,easy

AUTHOR

N. Sato, May 24 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, May 29 2004

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 29 22:26 EDT 2021. Contains 346346 sequences. (Running on oeis4.)