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%I #15 Nov 20 2022 08:35:07
%S 1,0,0,0,0,1,0,1,0,0,1,0,2,0,1,1,0,2,0,2,1,1,2,0,3,1,2,2,1,3,1,3,2,2,
%T 3,2,4,2,3,3,3,4,3,4,3,4,4,4,5,4,5,4,5,5,5,6,5,6,5,6,7,6,7,6,7,7,7,8,
%U 7,8,8,8,9,8,9,9,9,10,9,10
%N Expansion of 1/((1-x^5)*(1-x^7)*(1-x^12)).
%C a(n) is the number of partitions of n into parts 5, 7, and 12. - _Joerg Arndt_, Nov 20 2022
%H G. C. Greubel, <a href="/A025886/b025886.txt">Table of n, a(n) for n = 0..5000</a>
%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,1).
%F For n>23, a(n) = a(n-5) + a(n-7) - a(n-17) - a(n-19) + a(n-24). - _Harvey P. Dale_, Sep 28 2012
%t CoefficientList[Series[1/((1-x^5)(1-x^7)(1-x^12)),{x,0,80}],x] (* _Harvey P. Dale_, Sep 28 2012 *)
%t LinearRecurrence[{0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,-1,0,-1,0,0,0,0,1},{1,0,0,0,0,1, 0,1,0,0,1,0,2,0,1,1,0,2,0,2,1,1,2,0},80] (* _Harvey P. Dale_, Nov 02 2021 *)
%o (PARI) Vec(1/((1-x^5)*(1-x^7)*(1-x^12))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 27 2012
%o (Magma) R<x>:=PowerSeriesRing(Rationals(), 80); Coefficients(R!( 1/((1-x^5)*(1-x^7)*(1-x^12)) )); // _G. C. Greubel_, Nov 19 2022
%o (SageMath)
%o def A025886_list(prec):
%o P.<x> = PowerSeriesRing(ZZ, prec)
%o return P( 1/((1-x^5)*(1-x^7)*(1-x^12)) ).list()
%o A025886_list(80) # _G. C. Greubel_, Nov 19 2022
%Y Cf. A025882, A025883, A025884, A025885.
%K nonn,easy
%O 0,13
%A _N. J. A. Sloane_
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