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%I #12 Sep 08 2022 08:44:44
%S 1,23,365,4975,62661,753783,8811805,101107775,1145674421,12870591943,
%T 143722946445,1598128085775,17716831119781,195984586836503,
%U 2164626279788285,23881256748106975,263256769887630741
%N Expansion of 1/((1-4x)(1-8x)(1-11x)).
%H Vincenzo Librandi, <a href="/A019672/b019672.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 (23,-164,352).
%F a(n)= 11^(n+2)/21 -2*8^(n+1)/3 +4^(n+1)/7. - _R. J. Mathar_, Nov 11 2012
%F a(0)=1, a(1)=23, a(2)=365; for n>2, a(n) = 23*a(n-1) -164*a(n-2) +352*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 19*a(n-1) -88*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 8 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)*(1-8*x)*(1-11*x)))); /* or */ I:=[1, 23, 365]; [n le 3 select I[n] else 23*Self(n-1)-164*Self(n-2)+352*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Jul 03 2013
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_.
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