A028290 Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)).

1, 1, 2, 3, 4, 6, 8, 10, 14, 17, 22, 27, 33, 40, 48, 57, 68, 79, 93, 107, 124, 142, 162, 184, 209, 235, 265, 296, 331, 368, 409, 452, 500, 550, 605, 663, 726, 792, 864, 939, 1021, 1106, 1198, 1294, 1397, 1505

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Number of partitions of n into parts equal to 1, 2, 3, 5 and 8. E.g. a(5)=6 because we have 5, 3+2, 3+1+1, 2+2+1, 2+1+1+1 and 1+1+1+1+1. - Emeric Deutsch, Mar 25 2005

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,0,0,-1,1,0,0,-1,1,0,0,1,0,-1,-1,1).

Crossrefs

Cf. A003107, A029145.

Programs

Haskell

import Data.MemoCombinators (memo2, integral)
a028290 n = a028290_list !! n
a028290_list = map (p' 0) [0..] where
   p' = memo2 integral integral p
   p _ 0 = 1
   p 5 _ = 0
   p k m | m < parts !! k = 0
         | otherwise = p' k (m - parts !! k) + p' (k + 1) m
   parts = [1, 2, 3, 5, 8]
-- Reinhard Zumkeller, Dec 09 2015

Maple

G:=1/(1-x)/(1-x^2)/(1-x^3)/(1-x^5)/(1-x^8): Gser:=series(G,x=0,47): 1, seq(coeff(Gser,x^n),n=1..45); # Emeric Deutsch, Mar 25 2005

Mathematica

CoefficientList[ Series[ 1/Product[1 - x^Fibonacci[i], {i, 2, 6}], {x, 0, 45}], x] (* Robert G. Wilson v, Oct 15 2016 *)
CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)),{x,0,100}],x] (* Harvey P. Dale, Jan 26 2019 *)

PARI

Vec(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^5)*(1-x^8))+O(x^99)) \\ Charles R Greathouse IV, Sep 27 2012