%I #12 Sep 08 2022 08:44:44

%S 1,25,431,6365,86511,1117605,13957591,170189245,2038704671,

%T 24092243285,281680643751,3265150951725,37583315950831,

%U 430083097386565,4897580558961911,55540052099419805,627607236896972991

%N Expansion of 1/((1-4x)(1-10x)(1-11x)).

%H Vincenzo Librandi, <a href="/A019742/b019742.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (25,-194,440).

%F a(n) = 2*4^(n+1)/21 +11^(n+2)/7-5*10^(n+1)/3. - _R. J. Mathar_, Nov 11 2012

%F a(0)=1, a(1)=25, a(2)=431; for n>2, a(n) = 25*a(n-1) -194*a(n-2) +440*a(n-3). - _Vincenzo Librandi_, Jul 03 2013

%F a(n) = 21*a(n-1) -110*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013

%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 10 x) (1 - 11 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)

%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-10*x)*(1-11*x)))); /* or */ I:=[1,25,431]; [n le 3 select I[n] else 25*Self(n-1)-194*Self(n-2)+440*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.