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%I #12 May 17 2017 03:18:12
%S 1,1,1,2,2,2,3,3,4,6,6,7,9,9,10,12,13,15,18,19,21,24,25,27,31,33,36,
%T 41,43,46,51,53,57,63,66,71,78,81,86,93,97,103,111,116,123,132,137,
%U 144,154,160,168,179,186,195,207
%N Expansion of 1/((1-x)*(1-x^3)*(1-x^8)*(1-x^9)).
%C Number of partitions of n into parts 1, 3, 8 and 9. - _Ilya Gutkovskiy_, May 16 2017
%H G. C. Greubel, <a href="/A029054/b029054.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, 0, 1, 0, -1, -1, 0, 1, 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)=4, a(9)=6, a(10)=6, a(11)=7, a(12)=9, a(13)=9, a(14)=10, a(15)=12, a(16)=13, a(17)=15, a(18)=18, a(19)=19, a(20)=21, a(n)=a(n-1)+ a(n-3)- a(n-4)+ a(n-8)-a(n-10)-a(n-11)+a(n-13)-a(n-17)+a(n-18)+a(n-20)-a(n-21). - _Harvey P. Dale_, May 09 2013
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^8)(1-x^9)),{x,0,60}],x] (* or *) LinearRecurrence[{1,0,1,-1,0,0,0,1,0,-1,-1,0,1,0,0,0,-1,1,0,1,-1},{1,1,1,2,2,2,3,3,4,6,6,7,9,9,10,12,13,15,18,19,21},60] (* _Harvey P. Dale_, May 09 2013 *)
%o (PARI) x='x+O('x^50); Vec(1/((1-x)*(1-x^3)*(1-x^8)*(1-x^9))) \\ _G. C. Greubel_, May 17 2017
%K nonn
%O 0,4
%A _N. J. A. Sloane_
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