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 A221471 #14 Jan 02 2025 12:51:19
%S A221471 0,1,2,3,4,5,6,11,14,29,57,76,199,521,1364,3571,9349,24476,64079,
%T A221471 167761,439204,1149851,3010349,7881196,20633239,54018521,141422324,
%U A221471 370248451,969323029,2537720636,6643838879,17393796001,45537549124,119218851371
%N A221471 Integers n such that n^2 is the difference of two Lucas numbers (A000032).
%C A221471 This sequence, growing exponentially, is interesting because the corresponding sequence for Fibonacci numbers (A219114) appears to be finite. However, except the 7 numbers in A221472, it appears that the squares of all these numbers have the form 0, L(5) - L(0), or L(4n+2) - L(0), where L(n) denotes the n-th Lucas number.
%C A221471 It is easy to show that L(4n+2) - L(0) = L(2n+1)^2. - _Zhi-Wei Sun_, Jan 02 2015
%H A221471 T. D. Noe, <a href="/A221471/b221471.txt">Table of n, a(n) for n = 1..100</a>
%F A221471 Conjecture: a(n) = 3*a(n-1)-a(n-2) = A002878(n-8) for n>13. G.f.: x^2*(28*x^11-66*x^10-16*x^9-2*x^8-13*x^7-2*x^6-5*x^5-4*x^4-3*x^3-2*x^2-x+1) / (x^2-3*x+1). [_Colin Barker_, Feb 17 2013]
%t A221471 t = Union[Flatten[Abs[Table[LucasL[n] - LucasL[i], {n, 0, 120}, {i, n}]]]]; t2 = Select[t, IntegerQ[Sqrt[#]] &]; Sqrt[t2]
%Y A221471 Cf. A000032 (Lucas numbers), A113191 (difference of two Lucas numbers).
%Y A221471 Cf. A219114 (corresponding sequence for Fibonacci numbers).
%K A221471 nonn
%O A221471 1,3
%A A221471 _T. D. Noe_, Feb 13 2013