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 A156569 #13 Apr 18 2024 09:17:06
%S A156569 37,205,1193,6953,40525,236197,1376657,8023745,46765813,272571133,
%T A156569 1588660985,9259394777,53967707677,314546851285,1833313400033,
%U A156569 10685333548913,62278687893445,362986793811757,2115642074977097
%N A156569 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1)=37, a(2)=205.
%H A156569 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-1).
%F A156569 a(n) = ((34+7*sqrt(2))*(3-2*sqrt(2))^n+(34-7*sqrt(2))*(3+2*sqrt(2))^n)/4.
%F A156569 G.f.: x*(37-17*x)/(1-6*x+x^2). [corrected by _Klaus Brockhaus_, Sep 22 2009]
%F A156569 Limit_{n -> oo} a(n)/a(n-1) = 3+2*sqrt(2).
%t A156569 LinearRecurrence[{6,-1},{37,205},30] (* _Harvey P. Dale_, Aug 18 2014 *)
%o A156569 (PARI) {m=19; v=concat([37, 205], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}
%Y A156569 Third trisection of A156567.
%Y A156569 Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156568, A156570.
%K A156569 nonn,easy
%O A156569 1,1
%A A156569 _Klaus Brockhaus_, Feb 11 2009, Feb 16 2009