|
%I #16 Sep 08 2022 08:44:45
%S 1,23,371,5227,68955,877371,10927867,134329979,1637524859,19854820219,
%T 239894019963,2891817662331,34806527338363,418516051199867,
%U 5028894399547259,60400347075823483,725233079160063867
%N Expansion of 1/((1-x)(1-2x)(1-8x)(1-12x)).
%H Vincenzo Librandi, <a href="/A021279/b021279.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 (23,-158,328,-192).
%F a(n) = (21*12^(n+3) - 55*8^(n+3) + 154*2^(n+3) - 120)/9240. - _Yahia Kahloune_, Jul 08 2013
%F a(0)=1, a(1)=23, a(2)=371, a(3)=5227; for n >3, a(n) = 23*a(n-1) -158*a(n-2) +328*a(n-3) -192*a(n-4). - _Vincenzo Librandi_, Jul 08 2013
%F a(0)=1, a(1)=23; for n>1, a(n) = 20*a(n-1) -96*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013
%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 8 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)
%t LinearRecurrence[{23,-158,328,-192},{1,23,371,5227},30] (* _Harvey P. Dale_, Feb 11 2015 *)
%o (Magma) I:=[1, 23, 371, 5227]; [n le 4 select I[n] else 23*Self(n-1)-158*Self(n-2)+328*Self(n-3)-192*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-8*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 08 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
|
