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 A114040 #18 Dec 24 2023 09:37:09
%S A114040 1,9,49,281,1633,9513,55441,323129,1883329,10976841,63977713,
%T A114040 372889433,2173358881,12667263849,73830224209,430314081401,
%U A114040 2508054264193,14618011503753,85200014758321,496582077046169,2894292447518689,16869172608065961,98320743200877073
%N A114040 a(0) = 1, a(1) = 9, a(n) = 6*a(n-1) - a(n-2) - 4.
%C A114040 The most straightforward test for "triangularity" is istriangle(n) <===> issquare(8*n+1). If this sequence could be proved to be free of squares beyond the first three terms, that would lead directly to a proof that 0, 1 and 6 are the only triangular numbers whose squares are triangular numbers.
%H A114040 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F A114040 G.f.: (1+2x-7x^2)/((1-x)(1-6x+x^2)). [_R. J. Mathar_, Sep 09 2008]
%t A114040 LinearRecurrence[{7,-7,1},{1,9,49},30] (* _Harvey P. Dale_, Aug 18 2018 *)
%Y A114040 Equals 8*A001109(n)+1. It is also A081554(n)+1.
%K A114040 nonn
%O A114040 0,2
%A A114040 _N. J. A. Sloane_, based on email from Jack Brennen, Feb 01 2006