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 A089926 #19 Aug 27 2025 10:34:18
%S A089926 1,6,73,882,10657,128766,1555849,18798954,227143297,2744518518,
%T A089926 33161365513,400680904674,4841332221601,58496667563886,
%U A089926 706801342988233,8540112783422682,103188154744060417,1246797969712147686
%N A089926 a(n) = 12*a(n-1) + a(n-2), a(0)=1, a(1)=6.
%C A089926 The family of recurrences a(n) = 2*k*a(n-1) + a(n-2), a(0)=1, a(1)=k has solution a(n) = ((k+sqrt(k^2+1))^n + (k-sqrt(k^2+1))^n)/2; a(n) = Sum_{j=0..floor(n/2)} C(n,2k)*(k^2+1)^jk^(n-2j); a(n) = T(n,ki)*(-i)^n; e.g.f. exp(kx)*cosh(sqrt(k^2+1)*x).
%H A089926 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A089926 <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>
%H A089926 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,1).
%F A089926 E.g.f.: exp(6x)*cosh(sqrt(37)x);
%F A089926 a(n) = ((6+sqrt(37))^n + (6-sqrt(37))^n)/2;
%F A089926 a(n) = Sum_{k=0..floor(n/2)} C(n, 2k)*37^k*6^(n-2k).
%F A089926 a(n) = T(n, 6i)*(-i)^n with T(n, x) Chebyshev's polynomials of the first kind (see A053120) and i^2 = -1.
%F A089926 G.f.: (1-6x)/(1-12*x-x^2). - _Philippe Deléham_, Nov 21 2008
%Y A089926 Cf. A088320, A088317, A005667, A001077.
%Y A089926 Essentially the same as A041060.
%K A089926 easy,nonn,changed
%O A089926 0,2
%A A089926 _Paul Barry_, Nov 15 2003