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 A086302 #46 Apr 27 2025 12:31:20
%S A086302 8,120,528,1520,3480,6888,12320,20448,32040,47960,69168,96720,131768,
%T A086302 175560,229440,294848,373320,466488,576080,703920,851928,1022120,
%U A086302 1216608,1437600,1687400,1968408,2283120,2634128,3024120,3455880,3932288,4456320,5031048
%N A086302 a(n) = 4*n^4 + 24*n^3 + 48*n^2 + 36*n + 8.
%C A086302 Suppose one wishes to find sets of four positive integers (a,b,c,d) such that ab+1, ac+1, ad+1, bc+1, bd+1, cd+1 are perfect squares. Then one may take a = 1, b = x^2 + 2x, c = x^2 + 4x + 3, d = 4x^4 + 24x^3 + 48x^2 + 36x + 8.
%H A086302 Paolo Xausa, <a href="/A086302/b086302.txt">Table of n, a(n) for n = 0..10000</a>
%H A086302 Philip Gibbs, <a href="https://arxiv.org/abs/math/0107203">Diophantine quadruples and Cayley's hyperdeterminant</a>, arXiv:math/0107203 [math.NT], 2001.
%H A086302 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DiophantusProperty.html">Diophantus Property</a>.
%H A086302 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A086302 a(n) = A057769(n+1) + 1. - _N. J. A. Sloane_, Jun 12 2004
%F A086302 G.f.: 8*(1 + 10*x + x^2)/(1 - x)^5. - _Colin Barker_, Mar 26 2012
%F A086302 a(n) = 4 * (n+1) * (n+2) * (n^2 + 3*n + 1). - _Bruno Berselli_, Mar 26 2012
%F A086302 a(n) = 8*A062392(n+1). - _Bruce J. Nicholson_, Jun 05 2017
%F A086302 Sum_{n>=0} 1/a(n) = tan(sqrt(5)*Pi/2)*Pi/(4*sqrt(5)). - _Amiram Eldar_, Jan 22 2024
%F A086302 E.g.f.: 4*exp(x)*(2 + 28*x + 37*x^2 + 12*x^3 + x^4). - _Stefano Spezia_, Apr 27 2025
%e A086302 (a,b,c,d) = (1,3,8,120), (1,8,15,528), (1,15,24,1520), (1,24,35,3480), ...
%t A086302 LinearRecurrence[{5, -10, 10, -5, 1}, {8, 120, 528, 1520, 3480}, 50] (* or *)
%t A086302 A086302[n_] := 4 (n + 1) (n + 2) (n^2 + 3 n + 1);
%t A086302 Array[A086302, 50, 0] (* _Paolo Xausa_, Jan 16 2024 *)
%Y A086302 Cf. A057769, A062392.
%K A086302 nonn,easy
%O A086302 0,1
%A A086302 Neven Juric (neven.juric(AT)apis-it.hr), Aug 29 2003