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Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^9)).
1

%I #34 Sep 08 2022 08:44:50

%S 1,1,2,3,4,5,7,8,10,13,15,18,22,25,29,34,38,43,50,55,62,70,77,85,95,

%T 103,113,125,135,147,161,173,187,203,217,233,252,268,287,308,327,348,

%U 372,393,417,444,468,495,525,552,582,615,645,678,715,748,785,825,862,902,946,986,1030

%N Expansion of 1/((1-x)(1-x^2)(1-x^3)(1-x^9)).

%C Number of partitions of n into parts 1, 2, 3, and 9. - _Joerg Arndt_, Jul 07 2013

%H Vincenzo Librandi, <a href="/A029003/b029003.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1,0,0,1,-1,-1,0,1,1,-1).

%F G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^9)).

%F a(n) = floor(2/27*(floor(n/3) + 1)*cos(2*Pi*n/3) + (2*n^3 + 45*n^2 + 290*n + 744)/648). - _Tani Akinari_, Jul 07 2013

%t CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^3) (1 - x^9)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jan 22 2017 *)

%t LinearRecurrence[{1,1,0,-1,-1,1,0,0,1,-1,-1,0,1,1,-1},{1,1,2,3,4,5,7,8,10,13,15,18,22,25,29},70] (* _Harvey P. Dale_, Jul 17 2018 *)

%o (PARI) Vec(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^9))+O(x^66)) \\ _Joerg Arndt_, Jul 07 2013

%o (Magma) m:=60; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-x^2)*(1-x^3)*(1-x^9)))); // _Vincenzo Librandi_, Jan 22 2017

%K nonn

%O 0,3

%A _N. J. A. Sloane_