A029145 Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^8)).

1, 0, 1, 1, 1, 2, 2, 2, 4, 3, 5, 5, 6, 7, 8, 9, 11, 11, 14, 14, 17, 18, 20, 22, 25, 26, 30, 31, 35, 37, 41, 43, 48, 50, 55, 58, 63, 66, 72, 75, 82, 85, 92, 96, 103, 108, 115, 120, 129, 133, 143, 148, 157, 164, 173, 180

Offset

0,6

Comments

Number of partitions of n into parts 2, 3, 5, and 8. - Joerg Arndt, Jul 07 2013

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,0,0,-1,0,0,0,-1,0,0,0,1,1,0,-1).

Formula

a(n) = floor((2*n^3+54*n^2+435*n+2435+45*(n+1)*(-1)^n)/2880+1/4*(((-1)^n+floor((n+1)/4)-floor(n/4))*(-1)^floor(n/4))). - Tani Akinari, Jul 07 2013

a(n) = floor((173*n^3+63*n^2+48*n+320 - 9*(n+11)*(n mod 2))/288) - floor((3*n^3+n^2+2)/5). - Hoang Xuan Thanh, Sep 30 2025

Prog

(Haskell)
import Data.MemoCombinators (memo2, integral)
a029145 n = a029145_list !! n
a029145_list = map (p' 0) [0..] where
   p' = memo2 integral integral p
   p _ 0 = 1
   p 4 _ = 0
   p k m | m < parts !! k = 0
         | otherwise = p' k (m - parts !! k) + p' (k + 1) m
   parts = [2, 3, 5, 8]
-- Reinhard Zumkeller, Dec 09 2015
(PARI) a(n) = (n^3+27*n^2+240*n+1024 - 45*(n+11)*(n%2) + 288*((3*n^3+n^2+2)%5))\1440 \\ Hoang Xuan Thanh, Sep 30 2025

Crossrefs

Cf. A028290.

Sequence in context: A237598 A138241 A234615 * A238999 A097986 A368689

Adjacent sequences: A029142 A029143 A029144 * A029146 A029147 A029148

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved