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Expansion of 1/((1-x^3)(1-x^5)(1-x^6)(1-x^7)).
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%I #12 Feb 22 2024 20:22:00

%S 1,0,0,1,0,1,2,1,1,2,2,2,4,3,3,5,4,5,7,6,7,9,8,9,12,11,12,15,14,15,19,

%T 18,19,23,22,24,28,27,29,33,33,35,40,39,41,47,46,49,55,54,57,63,63,66,

%U 73,73,76,83,83,87,95,95

%N Expansion of 1/((1-x^3)(1-x^5)(1-x^6)(1-x^7)).

%C Number of partitions of n into parts 3, 5, 6, and 7. - _Vincenzo Librandi_, Jun 03 2014

%H Vincenzo Librandi, <a href="/A029272/b029272.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 (0, 0, 1, 0, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 0, 1, 0, 0, -1).

%F a(0)=1, a(1)=0, a(2)=0, a(3)=1, a(4)=0, a(5)=1, a(6)=2, a(7)=1, a(8)=1, a(9)=2, a(10)=2, a(11)=2, a(12)=4, a(13)=3, a(14)=3, a(15)=5, a(16)=4, a(17)=5, a(18)=7, a(19)=6, a(20)=7, a(n)=a(n-3)+a(n-5)+a(n-6)+a(n-7)-a(n-8)-a(n-9)- a(n-10)- a(n-11)-a(n-12)-a(n-13)+a(n-14)+a(n-15)+a(n-16)+a(n-18)-a(n-21). - _Harvey P. Dale_, Apr 08 2013

%t CoefficientList[Series[1/((1-x^3)(1-x^5)(1-x^6)(1-x^7)),{x,0,90}],x] (* or *) LinearRecurrence[{0,0,1,0,1,1,1,-1,-1,-1,-1,-1,-1,1,1,1,0,1,0,0,-1},{1,0,0,1,0,1,2,1,1,2,2,2,4,3,3,5,4,5,7,6,7},90] (* _Harvey P. Dale_, Apr 08 2013 *)

%K nonn,easy

%O 0,7

%A _N. J. A. Sloane_.