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%I #12 Dec 16 2018 19:57:59
%S 1,1,1,2,2,2,3,4,4,6,7,7,9,10,11,13,15,16,19,21,22,26,28,30,34,37,39,
%T 44,48,50,56,60,63,69,74,78,85,91,95,103,109,114,123,130,136,146,154,
%U 160,171,180,187,199,209,217,230
%N Expansion of 1/((1-x)(1-x^3)(1-x^7)(1-x^9)).
%C Number of partitions of n into parts 1, 3, 7 and 9. - _Ilya Gutkovskiy_, May 14 2017
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,0,1,-1,1,-2,1,-1,1,0,0,-1,1,0,1,-1).
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^7)(1-x^9)),{x,0,80}],x] (* or *) LinearRecurrence[{1,0,1,-1,0,0,1,-1,1,-2,1,-1,1,0,0,-1,1,0,1,-1},{1,1,1,2,2,2,3,4,4,6,7,7,9,10,11,13,15,16,19,21},80] (* _Harvey P. Dale_, Dec 16 2018 *)
%o (PARI) a(n)=floor((n+19)*(n^2+11*n+56)/1134+((n\3+1)*[1,1,-2]/27+[11,4,-18]/81)[n%3+1]) \\ _Tani Akinari_, May 20 2014
%K nonn
%O 0,4
%A _N. J. A. Sloane_.