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%I #21 Mar 24 2020 21:19:05
%S 1,1,1,2,2,3,4,4,5,7,8,9,11,12,14,17,18,20,24,26,29,33,35,39,44,47,51,
%T 57,61,66,73,77,83,91,96,103,112,118,126,136,143,152,163,171,181,194,
%U 203,214,228,238,251,266,277,291,308,321,336,354,368,385,405
%N Expansion of 1/((1-x)(1-x^3)(1-x^5)(1-x^9)).
%C Number of partitions of n into parts 1, 3, 5, and 9. - _Alois P. Heinz_, Oct 01 2014
%H <a href="/index/Rec#order_18">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,1,-1,0,-1,2,-1,0,-1,1,-1,1,0,1,-1).
%F a(n) = floor((n^3+27*n^2+204*n+700+10*[3*n+29,4,0][(n mod 3)+1])/810). - _Tani Akinari_, Oct 01 2014
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^5)(1-x^9)), {x, 0, 90}], x] (* _Jinyuan Wang_, Mar 24 2020 *)
%o (PARI) a(n)=round((n+9)*(n^2+18*n+52)/810+(n\3+1)*(3*!(n%3)-1)/27+[12,-5,-10][n%3+1]/81) \\ _Tani Akinari_, May 23 2014
%o (PARI) a(n)=(n^3+27*n^2+204*n+700+10*[3*n+29,4,0][n%3+1])\810 \\ _Tani Akinari_, Oct 01 2014
%o (PARI) Vec(1/((1-x)*(1-x^3)*(1-x^5)*(1-x^9)) + O(x^80)) \\ _Michel Marcus_, Oct 01 2014
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_