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 A011944 #44 Jun 06 2022 08:07:59
%S A011944 0,2,28,390,5432,75658,1053780,14677262,204427888,2847313170,
%T A011944 39657956492,552364077718,7693439131560,107155783764122,
%U A011944 1492487533566148,20787669686161950,289534888072701152
%N A011944 a(n) = 14*a(n-1) - a(n-2) with a(0) = 0, a(1) = 2.
%C A011944 Standard deviation of A011943.
%C A011944 Product x*y, where the pair (x, y) solves for x^2 - 3y^2 = 1, i.e., a(n)=A001075(n)*A001353(n). - _Lekraj Beedassy_, Jul 13 2006
%C A011944 Solutions m to the Diophantine equation where square m^2 = k*(k+1)/3, corresponding solutions k are in A007654. - _Bernard Schott_, Apr 10 2021
%C A011944 All solutions for y in Pell equation x^2 - 12*y^2 = 1. Corresponding values for x are in A011943. - _Herbert Kociemba_, Jun 05 2022
%H A011944 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A011944 E. Keith Lloyd, <a href="http://www.jstor.org/stable/3619201">The Standard Deviation of 1, 2,..., n: Pell's Equation and Rational Triangles</a>, Math. Gaz. vol 81 (1997), 231-243.
%H A011944 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-1).
%F A011944 For all members x of the sequence, 12*x^2 +1 is a square. Lim_{n->infinity} a(n)/a(n-1) = 7 + sqrt(12). - _Gregory V. Richardson_, Oct 13 2002
%F A011944 a(n) = ((7+2*sqrt(12))^(n-1) - (7-2*sqrt(12))^(n-1)) / (2*sqrt(12)). - _Gregory V. Richardson_, Oct 13 2002
%F A011944 a(n) = 13*(a(n-1) + a(n-2)) - a(n-3). a(n) = 15*(a(n-1) - a(n-2)) + a(n-3). - _Mohamed Bouhamida_, Sep 20 2006
%F A011944 a(n) = sinh(2n*arcsinh(sqrt(3)))/sqrt(12). - _Herbert Kociemba_, Apr 24 2008
%F A011944 G.f.: 2x/(1-14*x+x^2). - _Philippe Deléham_, Nov 17 2008
%t A011944 LinearRecurrence[{14,-1},{0,2},20] (* _Harvey P. Dale_, Oct 17 2019 *)
%t A011944 Table[2 ChebyshevU[-1 + n, 7], {n, 0, 18}] (* _Herbert Kociemba_, Jun 05 2022 *)
%Y A011944 a(n) = 2 * A007655 = {A001353(2n)}/2. Cf. A011943.
%Y A011944 Cf. A007654.
%K A011944 nonn,easy
%O A011944 0,2
%A A011944 E. K. Lloyd