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%I #15 Sep 08 2022 08:44:44
%S 1,22,332,4280,50736,571872,6238912,66567040,699159296,7259766272,
%T 74744097792,764616652800,7783588704256,78935331561472,
%U 798149140201472,8051859072450560,81081536382959616,815318946277097472
%N Expansion of 1/((1-4x)(1-8x)(1-10x)).
%H Vincenzo Librandi, <a href="/A019671/b019671.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 (22,-152,320).
%F a(n)= 2*4^n/3 -8^(n+1)+25*10^n/3 . - _R. J. Mathar_, Nov 11 2012
%F a(0)=1, a(1)=22, a(2)=332; for n>2, a(n) = 22*a(n-1) -152*a(n-2) +320*a(n-3). - _Vincenzo Librandi_, Jul 03 2013
%F a(n) = 18*a(n-1) -80*a(n-2) +4^n. - _Vincenzo Librandi_, Jul 03 2013
%t CoefficientList[Series[1 / ((1 - 4 x) (1 - 8 x) (1 - 10 x)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Jul 03 2013 *)
%t LinearRecurrence[{22,-152,320},{1,22,332},20] (* _Harvey P. Dale_, Aug 28 2013 *)
%o (Magma) m:=20; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-8*x)*(1-10*x)))); /* or */ I:=[1, 22, 332]; [n le 3 select I[n] else 22*Self(n-1)-152*Self(n-2)+320*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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