cp's OEIS Frontend

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

%I A029145 #17 Jul 08 2025 19:06:36
%S A029145 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,
%T A029145 35,37,41,43,48,50,55,58,63,66,72,75,82,85,92,96,103,108,115,120,129,
%U A029145 133,143,148,157,164,173,180
%N A029145 Expansion of 1/((1-x^2)(1-x^3)(1-x^5)(1-x^8)).
%C A029145 Number of partitions of n into parts 2, 3, 5, and 8. - _Joerg Arndt_, Jul 07 2013
%H A029145 Reinhard Zumkeller, <a href="/A029145/b029145.txt">Table of n, a(n) for n = 0..10000</a>
%H A029145 <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,0,0,-1,0,0,0,-1,0,0,0,1,1,0,-1).
%F A029145 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
%o A029145 (Haskell)
%o A029145 import Data.MemoCombinators (memo2, integral)
%o A029145 a029145 n = a029145_list !! n
%o A029145 a029145_list = map (p' 0) [0..] where
%o A029145    p' = memo2 integral integral p
%o A029145    p _ 0 = 1
%o A029145    p 4 _ = 0
%o A029145    p k m | m < parts !! k = 0
%o A029145          | otherwise = p' k (m - parts !! k) + p' (k + 1) m
%o A029145    parts = [2, 3, 5, 8]
%o A029145 -- _Reinhard Zumkeller_, Dec 09 2015
%Y A029145 Cf. A028290.
%K A029145 nonn,easy
%O A029145 0,6
%A A029145 _N. J. A. Sloane_