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 A133218 #17 Apr 02 2019 15:44:43
%S A133218 0,1,4,55,154,1885,5248,64051,178294,2175865,6056764,73915375,
%T A133218 205751698,2510946901,6989500984,85298279275,237437281774,
%U A133218 2897630548465,8065878079348,98434140368551,274002417416074,3343863141982285,9308016314067184,113592912687029155
%N A133218 Indices of triangular numbers (A000217) that are also decagonal (A001107).
%H A133218 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1, 34, -34, -1, 1).
%F A133218 For n>5, a(n) = 34*a(n-2) - a(n-4) + 16.
%F A133218 For n>6, a(n) = a(n-1) + 34*a(n-2) - 34*a(n-3) - a(n-4) + a(n-5).
%F A133218 For n>1, a(n) = 1/8 * ((4 + sqrt(2)*(-1)^n)*(1+sqrt(2))^(2*n - 3) + (4 - sqrt(2)*(-1)^n)*(1-sqrt(2))^(2*n-3) - 4).
%F A133218 a(n) = floor(1/8 * (4 + sqrt(2)*(-1)^n)* (1+sqrt(2))^(2*n-3)).
%F A133218 G.f.: x^2*(2*x^4+3*x^3-17*x^2-3*x-1)/((x-1)*(x^2+6*x+1)*(x^2-6*x+1)).
%F A133218 lim (n -> Infinity, a(2n+1)/a(2n)) = 1/7*(43 + 30*sqrt(2)).
%F A133218 lim (n -> Infinity, a(2n)/a(2n-1)) = 1/7*(11 + 6*sqrt(2)).
%e A133218 The third number which is both triangular (A000217) and decagonal (A001107) is A133216(3)=10. Since this is the fourth triangular number, we have a(3) = 4.
%t A133218 LinearRecurrence[{1, 34, -34, -1, 1 }, {0, 1, 4, 55, 154, 1885}, 24 ]
%Y A133218 Cf. A000217, A001107, A133216, A133217.
%K A133218 nonn
%O A133218 1,3
%A A133218 _Richard Choulet_, Oct 11 2007; _Ant King_, Nov 04 2011
%E A133218 Entry revised by _Max Alekseyev_, Nov 06 2011