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 A140766 #28 Jan 05 2025 04:23:07
%S A140766 1,5,24,114,540,2556,12096,57240,270864,1281744,6065280,28701216,
%T A140766 135815616,642686400,3041224704,14391229824,68100030720,322252805376,
%U A140766 1524916647936,7215983055360,34146398444544,161582492335104,764616563343360,3618204426049536
%N A140766 a(n) = 6*a(n-1) - 6*a(n-2).
%C A140766 Companion sequence = A030192 beginning (1, 6, 30, 144, 684,...).
%H A140766 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-6).
%F A140766 a(n) = 6*a(n-1) - 6*a(n-2); a(1) = 1, a(2) = 5.
%F A140766 Term (1,1) of M^n, where M = the 3x3 matrix [1,1,1; 1,2,1; 3,1,3].
%F A140766 From _R. J. Mathar_, May 31 2008: (Start)
%F A140766 O.g.f.: x*(1 - x)/(1 - 6*x + 6*x^2).
%F A140766 a(n) = A030192(n-1) - A030192(n-2). (End)
%F A140766 a(n) = Sum_{1<=k<=n} A030523(n,k)*2^(k-1). - _Philippe Deléham_, Feb 19 2013
%F A140766 a(n) = (sqrt(3)/36)*((3 + sqrt(3))^(n+1) - (3 - sqrt(3))^(n+1)). - _Taras Goy_, Jan 03 2025
%F A140766 E.g.f.: (exp(3*x)*(cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)) - 1)/6. - _Stefano Spezia_, Jan 04 2025
%e A140766 a(5) = 540 = 6*a(4) - 6*a(3) = 6*(114) - 6*24.
%e A140766 a(5) = 540 = term (1,1) of X^5.
%t A140766 LinearRecurrence[{6,-6},{1,5},30] (* _Harvey P. Dale_, Oct 01 2014 *)
%Y A140766 Cf. A030192, A030523.
%K A140766 nonn,easy
%O A140766 1,2
%A A140766 _Gary W. Adamson_ and _Roger L. Bagula_, May 28 2008
%E A140766 More terms from _R. J. Mathar_, May 31 2008
%E A140766 More terms from _Harvey P. Dale_, Oct 01 2014