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%I #42 Feb 08 2024 03:12:10
%S 1,10,76,520,3376,21280,131776,807040,4907776,29708800,179301376,
%T 1080002560,6496792576,39047864320,234555621376,1408407470080,
%U 8454739787776,50745618595840,304542431051776
%N Expansion of 1/((1-4*x)*(1-6*x)).
%H Vincenzo Librandi, <a href="/A016149/b016149.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-24).
%F a(n) = 10*a(n-1)-24*a(n-2) for n>1, a(0)=1. - _Barry E. Williams_, Jan 13 2000
%F a(n) = ((6^(n+1))-4^(n+1))/2. - _Barry E. Williams_, Jan 13 2000
%F a(n) = A081199(n+1). Binomial transform of A080961. - _R. J. Mathar_, Sep 18 2008
%F a(n) = Sum_{k=0..n} 6^k*4^(n-k). [_Bruno Berselli_, Aug 07 2013]
%p seq(add(2^(2*n-k)*binomial(n,k)/2,k=1..n),n=1..19); # _Zerinvary Lajos_, Apr 18 2009
%t Join[{a=1,b=10},Table[c=10*b-24*a;a=b;b=c,{n,60}]] (* _Vladimir Joseph Stephan Orlovsky_, Jan 27 2011 *)
%t LinearRecurrence[{10,-24},{1,10},30] (* or *) CoefficientList[ Series[ 1/(1-10 x+24 x^2),{x,0,30}],x] (* _Harvey P. Dale_, Apr 24 2011 *)
%o (Sage) [lucas_number1(n,10,24) for n in range(1, 20)]# _Zerinvary Lajos_, Apr 26 2009]
%o (PARI) Vec(1/((1-4*x)*(1-6*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 24 2012
%o (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)))); // _Vincenzo Librandi_, Jun 24 2013
%Y Cf. A081199, A080961.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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