A017997 - OEIS

%I #19 Sep 08 2022 08:44:44

%S 1,18,223,2364,23053,213654,1914571,16756128,144132505,1223664090,

%T 10283600119,85728989892,710053773157,5849984757726,47986764852067,

%U 392202340697256,3195776321789809,25973313876940962

%N Expansion of 1/((1-3x)(1-7x)(1-8x)).

%H Vincenzo Librandi, <a href="/A017997/b017997.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 (18,-101,168).

%F a(n) = (4*8^(n+2) - 5*7^(n+2) + 3^(n+2))/20. [_Yahia Kahloune_, Jun 30 2013]

%F a(0)=1, a(1)=18, a(2)=223; for n>2, a(n) = 18*a(n-1) -101*a(n-2) +168*a(n-3). - _Vincenzo Librandi_, Jul 02 2013

%F a(n) = 15*a(n-1) -56*a(n-2) +3^n. - _Vincenzo Librandi_, Jul 02 2013

%t CoefficientList[Series[1 / ((1 - 3 x) (1 - 7 x) (1 - 8 x)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jul 02 2013 *)

%t LinearRecurrence[{18,-101,168},{1,18,223},20] (* _Harvey P. Dale_, Jan 01 2022 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-7*x)*(1-8*x)))); /* or */ I:=[1, 18, 223]; [n le 3 select I[n] else 18*Self(n-1)-101*Self(n-2)+168*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 02 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.