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%I #14 Sep 08 2022 08:44:45
%S 1,16,173,1592,13461,108192,841261,6392584,47771141,352537328,
%T 2576599389,18689228376,134742802741,966708860224,6908017500557,
%U 49202455443368,349495185871461,2476934287969680,17521347937528765
%N Expansion of 1/((1-x)(1-2x)(1-6x)(1-7x)).
%H Vincenzo Librandi, <a href="/A021174/b021174.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (16,-83,152,-84).
%F a(0)=1, a(1)=16, a(2)=173, a(3)=1592; for n>3, a(n) = 16*a(n-1) -83*a(n-2) +152*a(n-3) -84*a(n-4). - _Vincenzo Librandi_, Jul 07 2013
%F a(0)=1, a(1)=16; for n>1, a(n) = 13*a(n-1) -42*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 07 2013
%F a(n) = (2*7^(n+3) - 3*6^(n+3) + 3*2^(n+3) - 2)/60. [_Yahia Kahloune_, Jul 07 2013]
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 6 x) (1 - 7 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 07 2013 *)
%t LinearRecurrence[{16,-83,152,-84},{1,16,173,1592},20] (* _Harvey P. Dale_, May 29 2019 *)
%o (Magma) I:=[1, 16, 173, 1592]; [n le 4 select I[n] else 16*Self(n-1)-83*Self(n-2)+152*Self(n-3)-84*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-6*x)*(1-7*x)))); // _Vincenzo Librandi_, Jul 07 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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