A029068 - OEIS

%I #13 Aug 08 2025 00:48:44

%S 1,1,1,1,2,3,3,3,4,5,6,7,8,9,10,12,14,15,16,18,21,23,25,27,30,33,36,

%T 39,42,45,49,53,57,61,65,70,75,80,85,90,96,102,108,114,121,128,135,

%U 142,150,158,166,174,183,192,201

%N Expansion of 1/((1-x)*(1-x^4)*(1-x^5)*(1-x^11)).

%C Number of partitions of n into parts 1, 4, 5 and 11. - _Ilya Gutkovskiy_, May 17 2017

%H G. C. Greubel, <a href="/A029068/b029068.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,0,-1,0,0,-1,1,1,-1,0,0, -1,0,1,0,0,1,-1).

%F a(n) = floor((2*n^3 + 63*n^2 + 580*n + 88*(-1)^n + 2760)/2640 + (1/5)*((-1)^[(n mod 5)>1] + [(n mod 5)=2])). - _Hoang Xuan Thanh_, Aug 06 2025

%t CoefficientList[Series[1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^11)), {x, 0, 50}], x] (* _G. C. Greubel_, May 17 2017 *)

%o (PARI) my(x='x+O('x^50)); Vec(1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^11))) \\ _G. C. Greubel_, May 17 2017

%o (PARI) a(n) = floor((2*n^3 + 63*n^2 + 580*n + 88*(-1)^n + 2760)/2640 + (1/5)*[1,1,0,-1,-1][n%5+1]) \\ _Hoang Xuan Thanh_, Aug 06 2025

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_