A025902 - OEIS

%I #12 Jan 23 2024 02:16:13

%S 1,0,0,0,0,0,1,0,1,1,0,0,1,0,1,1,1,1,2,0,1,1,1,1,3,1,2,2,1,1,3,1,3,3,

%T 2,2,4,1,3,3,3,3,5,2,4,4,3,3,6,3,5,5,4,4,7,3,6,6,5,5,8,4,7,7,6,6,9,5,

%U 8,8,7,7,11,6,9,9,8,8,12,7

%N Expansion of 1/((1-x^6)*(1-x^8)*(1-x^9)).

%C a(n) is the number of partitions of n into parts 6, 8, and 9. - _Michel Marcus_, Jan 23 2024

%H G. C. Greubel, <a href="/A025902/b025902.txt">Table of n, a(n) for n = 0..5000</a>

%H <a href="/index/Rec#order_23">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1,0,1,1,0,0,0,0,-1,-1,0,-1,0,0,0,0,0,1).

%t CoefficientList[ Series[1/((1-x^6)*(1-x^8)*(1-x^9)), {x,0,100}], x] (* _G. C. Greubel_, Jan 23 2024 *)

%o (Magma) R<x>:=PowerSeriesRing(Integers(), 100); Coefficients(R!( 1/((1-x^6)*(1-x^8)*(1-x^9)) )); // _G. C. Greubel_, Jan 23 2024

%o (SageMath)

%o def A025902_list(prec):

%o     P.<x> = PowerSeriesRing(ZZ, prec)

%o     return P( 1/((1-x^6)*(1-x^8)*(1-x^9))).list()

%o A025902_list(100) # _G. C. Greubel_, Jan 23 2024

%Y Cf. A025896, A025897, A025898, A025899, A025900, A025901, A025903.

%K nonn

%O 0,19

%A _N. J. A. Sloane_