A021254 - OEIS

%I #16 Sep 08 2022 08:44:45

%S 1,22,341,4646,59661,743358,9112405,110693878,1337742173,16118816558,

%T 193887174117,2329875721446,27981116089837,335931645121822,

%U 4032287505801077,48395204420052950,580796733493846653

%N Expansion of 1/((1-x)(1-2x)(1-7x)(1-12x)).

%H Vincenzo Librandi, <a href="/A021254/b021254.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 (22,-143,290,-168).

%F a(n) = (3*12^(n+3) - 11*7^(n+3) + 33*2^(n+3) - 25)/1650. [_Yahia Kahloune_, Jul 07 2013]

%F a(0)=1, a(1)=22, a(2)=341, a(3)=4646; for n>3, a(n) = 22*a(n-1) -143*a(n-2) +290*a(n-3) -168*a(n-4). - _Vincenzo Librandi_, Jul 08 2013

%F a(0)=1, a(1)=22; for n>1, a(n) = 19*a(n-1) -84*a(n-2) +2^n -1. - _Vincenzo Librandi_, Jul 08 2013

%t CoefficientList[Series[1 / ((1 - x) (1 - 2 x) (1 - 7 x) (1 - 12 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 08 2013 *)

%t LinearRecurrence[{22,-143,290,-168},{1,22,341,4646},30] (* _Harvey P. Dale_, Jul 22 2013 *)

%o (Magma) I:=[1, 22, 341, 4646]; [n le 4 select I[n] else 22*Self(n-1)-143*Self(n-2)+290*Self(n-3)-168*Self(n-4): n in [1..25]]; /* or */ m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)*(1-2*x)*(1-7*x)*(1-12*x)))); // _Vincenzo Librandi_, Jul 08 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.