A029051 - OEIS

%I #15 May 14 2017 08:00:54

%S 1,1,1,2,2,2,3,4,4,5,7,7,8,10,11,12,14,16,17,19,22,24,26,29,32,34,37,

%T 41,44,47,52,56,59,64,69,73,78,84,89,94,101,107,113,120,127,134,141,

%U 149,157,165,174,183,192,201,211

%N Expansion of 1/((1-x)(1-x^3)(1-x^7)(1-x^10)).

%C Number of partitions of n into parts 1, 3, 7 and 10. - _Ilya Gutkovskiy_, May 14 2017

%H Alois P. Heinz, <a href="/A029051/b029051.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, 1, -1, 0, 0, 1, -1, 0, 0, 0, 0, -1, 1, 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)=4, a(8)=4, a(9)=5, a(10)=7, a(11)=7, a(12)=8, a(13)=10, a(14)=11, a(15)=12, a(16)=14, a(17)=16, a(18)=17, a(19)=19, a(20)=22, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-7)-a(n-8)- a(n-13)+ a(n-14)-a(n-17)+a(n-18)+a(n-20)-a (n-21). - _Harvey P. Dale_, May 06 2013

%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^7)(1-x^10)),{x,0,70}],x] (* or *) LinearRecurrence[{1,0,1,-1,0,0,1,-1,0,0,0,0,-1,1,0,0,-1,1,0,1,-1},{1,1,1,2,2,2,3,4,4,5,7,7,8,10,11,12,14,16,17,19,22},70] (* _Harvey P. Dale_, May 06 2013 *)

%o (PARI) a(n)=floor((2*n^3+63*n^2+582*n+2456)/2520+2*((n%10<1)-(n%10>8))/5+(n+1)%3/9) \\ _Tani Akinari_, May 31 2014

%K nonn

%O 0,4

%A _N. J. A. Sloane_.