|
%I #11 Jul 30 2015 23:00:51
%S 1,1,2,3,4,5,7,8,10,12,15,17,21,24,28,32,37,41,47,52,59,65,73,80,89,
%T 97,107,116,127,137,150,161,175,188,203,217,234,249,267,284,304,322,
%U 344,364,387,409,434,457,484,509
%N Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^10)).
%C Number of partitions of n into parts 1, 2, 3, and 10. [_Joerg Arndt_, Jul 07 2013]
%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, 0, -1, -1, 1, 0, 0, 0, 1, -1, -1, 0, 1, 1, -1).
%F a(0)=1, a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(6)=7, a(7)=8, a(8)=10, a(9)=12, a(10)=15, a(11)=17, a(12)=21, a(13)=24, a(14)=28, a(15)=32, a(n)=a(n-1)+a(n-2)-a(n-4)-a(n-5)+a(n-6)+a(n-10)-a(n-11)- a(n-12)+ a(n-14)+a(n-15)-a(n-16). - _Harvey P. Dale_, Jun 01 2013
%F a(n) = floor((2*n^3+48*n^2+327*n+927+9*(n+1)*(-1)^n)/720). - _Tani Akinari_, Jul 07 2013
%t CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^10)),{x,0,60}],x] (* or *) LinearRecurrence[{1,1,0,-1,-1,1,0,0,0,1,-1,-1,0,1,1,-1},{1,1,2,3,4,5,7,8,10,12,15,17,21,24,28,32},60] (* _Harvey P. Dale_, Jun 01 2013 *)
%K nonn
%O 0,3
%A _N. J. A. Sloane_.
|
