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A028290 Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

Conjecture: satisfies a linear recurrence having signature (1, 1, 0, -1, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, 0, -1, -1, 1). - Harvey P. Dale, Jan 26 2019

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

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 *)

PROG

(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

(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

CROSSREFS

Cf. A003107, A029145.

Sequence in context: A239100 A243225 A220851 * A003107 A217123 A014977

Adjacent sequences:  A028287 A028288 A028289 * A028291 A028292 A028293

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 18 00:19 EST 2019. Contains 320237 sequences. (Running on oeis4.)