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 A094347 #40 Dec 21 2023 11:57:41
%S A094347 2,2,26,362,5042,70226,978122,13623482,189750626,2642885282,
%T A094347 36810643322,512706121226,7141075053842,99462344632562,
%U A094347 1385331749802026,19295182152595802,268747218386539202,3743165875258953026
%N A094347 a(n) = 14*a(n-1) - a(n-2); a(0) = a(1) = 2.
%C A094347 Even x satisfying the Pellian x^2 - 3*y^2 = 1. For corresponding y see A028230.
%H A094347 Michael De Vlieger, <a href="/A094347/b094347.txt">Table of n, a(n) for n = 0..874</a>
%H A094347 Christian Aebi and Grant Cairns, <a href="https://arxiv.org/abs/2312.10866">Less than Equable Triangles on the Eisenstein lattice</a>, arXiv:2312.10866 [math.CO], 2023.
%H A094347 R. K. Guy, <a href="/A001075/a001075.pdf">Letter to N. J. A. Sloane concerning A001075, A011943, A094347</a> [Scanned and annotated letter, included with permission]
%H A094347 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A094347 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-1).
%F A094347 G.f.: 2*(1 - 13*x)/(1 - 14*x + x^2). [_Philippe Deléham_, Nov 17 2008]
%F A094347 a(n) = ((2 + sqrt(3))^(2*n - 1) + (2 - sqrt(3))^(2*n - 1))/2. - _Gerry Martens_, Jun 03 2015
%F A094347 a(n) = (1/2)*sqrt(4 + (-2*sqrt(-2 + (7 - 4*sqrt(3))^(2*n) + (7 + 4*sqrt(3))^(2*n)) + sqrt(3)*sqrt(2 + (7 - 4*sqrt(3))^(2*n) + (7 + 4*sqrt(3))^(2*n)))^2). - _Gerry Martens_, Jun 03 2015
%F A094347 E.g.f.: exp(7*x)*(2*cosh(4*sqrt(3)*x) - sqrt(3)*sinh(4*sqrt(3)*x)). - _Franck Maminirina Ramaharo_, Nov 12 2018
%t A094347 LinearRecurrence[{14,-1},{2,2},40] (* or *) CoefficientList[ Series[2(1-13x)/(1-14x+x^2),{x,0,39}],x] (* _Harvey P. Dale_, Apr 23 2011 *)
%o A094347 (Maxima) (a[0]:2, a[1]:2, a[n] := 14*a[n - 1] - a[n-2], makelist(a[n], n, 0, 50)); /* _Franck Maminirina Ramaharo_, Nov 12 2018 */
%Y A094347 a(n) = 2*A001570(n).
%Y A094347 Bisection of A001075.
%Y A094347 Cf. A028230.
%K A094347 nonn,easy
%O A094347 0,1
%A A094347 _Lekraj Beedassy_, Jun 03 2004
%E A094347 Corrected by _Lekraj Beedassy_, Jun 11 2004