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 A233450 #30 Jun 13 2015 00:54:55
%S A233450 0,1,6,15,64,153,638,1519,6320,15041,62566,148895,619344,1473913,
%T A233450 6130878,14590239,60689440,144428481,600763526,1429694575,5946945824,
%U A233450 14152517273,58868694718,140095478159,582740001360,1386802264321,5768531318886,13727927165055
%N A233450 Numbers n such that 3*T(n)+1 is a square, where T = A000217.
%C A233450 For n>1, partial sums of A080872 starting from A080872(1).
%H A233450 Bruno Berselli, <a href="/A233450/b233450.txt">Table of n, a(n) for n = 1..200</a>
%H A233450 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10,-1,1).
%F A233450 G.f.: x^2*(1 + 5*x - x^2 - x^3) / ((1 - x)*(1 - 10*x^2 + x^4)).
%F A233450 a(n) = a(n-1) +10*a(n-2) -10*a(n-3) -a(n-4) +a(n-5) for n>5, a(1)=0, a(2)=1, a(3)=6, a(4)=15, a(5)=64.
%F A233450 a(n) = -1/2 + ( (-3*(-1)^n + 2*sqrt(6))*(5 + 2*sqrt(6))^floor(n/2) - (3*(-1)^n + 2*sqrt(6))*(5 - 2*sqrt(6))^floor(n/2) )/12.
%e A233450 153 is in the sequence because 3*153*154/2+1 = 188^2.
%t A233450 LinearRecurrence[{1, 10, -10, -1, 1}, {0, 1, 6, 15, 64}, 30]
%Y A233450 Sequence A129444 gives n+1.
%Y A233450 Cf. A000217, A080872, A129445 (square roots of 3*A000217(a(n))+1), A132596 (numbers m such that 3*A000217(m) is a square).
%Y A233450 Cf. numbers m such that k*A000217(m)+1 is a square: A006451 for k=1; m=0 for k=2; this sequence for k=3; A001652 for k=4; A129556 for k=5; A001921 for k=6.
%K A233450 nonn,easy
%O A233450 1,3
%A A233450 _Bruno Berselli_, Dec 10 2013