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 A028231 #42 Feb 28 2018 04:52:03
%S A028231 1,22,313,4366,60817,847078,11798281,164328862,2288805793,31878952246,
%T A028231 444016525657,6184352406958,86136917171761,1199732487997702,
%U A028231 16710117914796073,232741918319147326,3241676738553266497,45150732421426583638,628868577161418904441
%N A028231 From hexagons in a circle problem.
%C A028231 Numbers k such that (k^2 + k + 1)/3 is a square. - _Arkadiusz Wesolowski_, Feb 10 2012
%C A028231 Given by the numerators of the convergents to the continued fraction [1,(1,2)^i,3,(1,2)^{i-1},1]. - _Jeffrey Shallit_, Dec 11 2017
%D A028231 J. D. E. Konhauser et al., Which Way Did the Bicycle Go?, MAA 1996, p. 104.
%D A028231 T. Nagell, Des équations indéterminées x^2 + x + 1 = y^n et x^2 + x + 1 = 3*y^n, Norsk Mat. Forenings Skrifter, Ser. I, (1921).
%H A028231 Michel Marcus, <a href="/A028231/b028231.txt">Table of n, a(n) for n = 0..100</a>
%H A028231 Kevin A. Broughan, <a href="https://www.emis.de/journals/INTEGERS/papers/m15/m15.Abstract.html">An explicit bound for aliquot cycles of repdigits</a>, #A15 INTEGERS Vol 12 (2012) p. 4.
%H A028231 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (15,-15,1)
%F A028231 a(n) = sqrt(3)*((2+sqrt(3))^(2*n+1) - (2-sqrt(3))^(2*n+1))/4 - 1/2 (see Kevin A. Broughan paper). - _Michel Marcus_, Jul 28 2012
%F A028231 a(n) = 15*a(n-1)-15*a(n-2)+a(n-3). G.f.: (1+7*x-2*x^2)/((1-x)*(1-14*x+x^2)). - conjectured by _Colin Barker_, Apr 10 2012; these follow easily from the formula.
%p A028231 f:= gfun:-rectoproc({a(n) = 15*a(n-1)-15*a(n-2)+a(n-3),a(0)=1,a(1)=22,a(2)=313},a(n),remember):
%p A028231 map(f, [$0..30]); # _Robert Israel_, Dec 12 2017
%t A028231 With[{k = Sqrt@ 3}, Simplify@ Array[k ((2 + k)^(2 # + 1) - (2 - k)^(2 # + 1))/4 - 1/2 &, 19, 0]] (* _Michael De Vlieger_, Dec 11 2017 *)
%o A028231 (PARI) a(n) = {w = quadgen(12);w*((2+w)^(2*n+1) - (2-w)^(2*n+1))/4 - 1/2;} /* _Michel Marcus_, Jul 28 2012 */
%Y A028231 Cf. A001570, which gives the corresponding values of y in 3y^2 = n^2 + n + 1. - _Jeffrey Shallit_, Dec 11 2017
%K A028231 nonn,easy
%O A028231 0,2
%A A028231 _N. J. A. Sloane_
%E A028231 Edited by _Robert Israel_, Dec 12 2017