cp's OEIS Frontend

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

%I A028290 #22 Jul 08 2025 18:32:06
%S A028290 1,1,2,3,4,6,8,10,14,17,22,27,33,40,48,57,68,79,93,107,124,142,162,
%T A028290 184,209,235,265,296,331,368,409,452,500,550,605,663,726,792,864,939,
%U A028290 1021,1106,1198,1294,1397,1505
%N A028290 Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^5)(1-x^8)).
%C A028290 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
%H A028290 Reinhard Zumkeller, <a href="/A028290/b028290.txt">Table of n, a(n) for n = 0..10000</a>
%H A028290 <a href="/index/Rec#order_19">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,0,0,-1,1,0,0,-1,1,0,0,1,0,-1,-1,1).
%p A028290 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
%t A028290 CoefficientList[ Series[ 1/Product[1 - x^Fibonacci[i], {i, 2, 6}], {x, 0, 45}], x] (* _Robert G. Wilson v_, Oct 15 2016 *)
%t A028290 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 *)
%o A028290 (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
%o A028290 (Haskell)
%o A028290 import Data.MemoCombinators (memo2, integral)
%o A028290 a028290 n = a028290_list !! n
%o A028290 a028290_list = map (p' 0) [0..] where
%o A028290    p' = memo2 integral integral p
%o A028290    p _ 0 = 1
%o A028290    p 5 _ = 0
%o A028290    p k m | m < parts !! k = 0
%o A028290          | otherwise = p' k (m - parts !! k) + p' (k + 1) m
%o A028290    parts = [1, 2, 3, 5, 8]
%o A028290 -- _Reinhard Zumkeller_, Dec 09 2015
%Y A028290 Cf. A003107, A029145.
%K A028290 nonn,easy
%O A028290 0,3
%A A028290 _N. J. A. Sloane_