This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A016149 #54 Aug 05 2024 02:37:22
%S A016149 1,10,76,520,3376,21280,131776,807040,4907776,29708800,179301376,
%T A016149 1080002560,6496792576,39047864320,234555621376,1408407470080,
%U A016149 8454739787776,50745618595840,304542431051776,1827529464217600,10966276296933376,65802055828111360,394829927154712576
%N A016149 Expansion of g.f. 1/((1 - 4*x)*(1 - 6*x)).
%H A016149 Vincenzo Librandi, <a href="/A016149/b016149.txt">Table of n, a(n) for n = 0..200</a>
%H A016149 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-24).
%F A016149 From _Barry E. Williams_, Jan 13 2000: (Start)
%F A016149 a(n) = 10*a(n-1) - 24*a(n-2) for n>1, a(0)=1.
%F A016149 a(n) = ((6^(n+1)) - 4^(n+1))/2. (End)
%F A016149 a(n) = A081199(n+1). Binomial transform of A080961. - _R. J. Mathar_, Sep 18 2008
%F A016149 a(n) = Sum_{k=0..n} 6^k*4^(n-k). - _Bruno Berselli_, Aug 07 2013
%F A016149 E.g.f.: exp(4*x)*(3*exp(2*x) - 2). - _Stefano Spezia_, Jul 23 2024
%p A016149 seq(add(2^(2*n-k)*binomial(n,k)/2,k=1..n),n=1..19); # _Zerinvary Lajos_, Apr 18 2009
%t A016149 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 A016149 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 A016149 (SageMath) [lucas_number1(n,10,24) for n in range(1, 20)] # _Zerinvary Lajos_, Apr 26 2009
%o A016149 (PARI) Vec(1/((1-4*x)*(1-6*x))+O(x^99)) \\ _Charles R Greathouse IV_, Sep 24 2012
%o A016149 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-4*x)*(1-6*x)))); // _Vincenzo Librandi_, Jun 24 2013
%Y A016149 Cf. A081199, A080961.
%K A016149 nonn,easy
%O A016149 0,2
%A A016149 _N. J. A. Sloane_