|
%I #16 May 17 2017 03:18:46
%S 1,1,1,2,2,2,3,3,3,4,5,6,7,8,9,10,11,12,13,14,16,18,20,22,24,26,28,30,
%T 32,34,37,40,43,47,50,53,57,60,63,67,71,75,80,85,90,95,100,105,110,
%U 115,121,127,133,140,147,154
%N Expansion of 1/((1-x)*(1-x^3)*(1-x^10)*(1-x^11)).
%C Number of partitions of n into parts 1, 3, 10 and 11. - _Ilya Gutkovskiy_, May 16 2017
%H Alois P. Heinz, <a href="/A029060/b029060.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_25">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,0,0,0,0,1,0,-1,-1,0,1, 0,0,0,0,0,-1,1,0,1,-1).
%F a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=2, a(6)=3, a(7)=3, a(8)=3, a(9)=4, a(10)=5, a(11)=6, a(12)=7, a(13)=8, a(14)=9, a(15)=10, a(16)=11, a(17)=12, a(18)=13, a(19)=14, a(20)=16, a(21)=18, a(22)=20, a(23)=22, a(24)=24, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-10)-a(n-12)-a(n-13)+a(n-15)- a(n-21)+ a(n-22)+a(n-24)-a(n-25). - _Harvey P. Dale_, Jan 11 2014
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^10)(1-x^11)),{x,0,60}],x] (* or *) LinearRecurrence[ {1,0,1,-1,0,0,0,0,0,1,0,-1,-1,0,1,0,0,0,0,0,-1,1,0,1,-1}, {1,1,1,2,2,2,3,3,3,4,5,6,7,8,9,10,11,12,13,14,16,18,20, 22,24},60] (* _Harvey P. Dale_, Jan 11 2014 *)
%o (PARI) a(n)=floor((2*n^3+75*n^2+822*n+4312)/3960+[-1,-1,-1,1,1,1,2,1,-1,-2][n%10+1]/5+((2*n+2)%3-1)/9) \\ _Tani Akinari_, May 22 2014
%o (PARI) x='x+O('x^50); Vec(1/((1-x)*(1-x^3)*(1-x^10)*(1-x^11))) \\ _G. C. Greubel_, May 17 2017
%K nonn
%O 0,4
%A _N. J. A. Sloane_
|
