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 A002537 M3409 N1379 #37 Jul 02 2025 16:01:54
%S A002537 1,1,4,11,23,79,148,533,977,3553,6484,23627,43079,157039,286276,
%T A002537 1043669,1902497,6936001,12643492,46094987,84025463,306335887,
%U A002537 558412276,2035832213,3711069041,13529634721,24662841844,89914587851
%N A002537 a(2n) = a(2n-1) + 3a(2n-2), a(2n+1) = 2a(2n) + 3a(2n-1).
%D A002537 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002537 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%D A002537 A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.
%H A002537 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A002537 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A002537 R. C. Read, <a href="/A000684/a000684_1.pdf">Letter to N. J. A. Sloane, Oct. 29, 1976</a>
%H A002537 Albert Tarn, <a href="/A001333/a001333_1.pdf">Approximations to certain square roots and the series of numbers connected therewith</a> [Annotated scanned copy]
%H A002537 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 8, 0, -9).
%F A002537 a(n)=8a(n-2)-9a(n-4). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
%F A002537 G.f.: (1+x-4x^2+3x^3)/(1-8x^2+9x^4). a(n)/A002536(n) converges to sqrt(7). - Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
%F A002537 a(n+1) = x^n + (-1)^n*(x-2)^n where x = (1+sqrt(7)) and the term is divided by 2 for a(2) and a(3), 4 for a(4) and a(5)... 2^n for a(2n) and a(2n+1). - _Ben Paul Thurston_, Aug 30 2006
%p A002537 A002537:=(1+z-4*z**2+3*z**3)/(1-8*z**2+9*z**4); # conjectured by _Simon Plouffe_ in his 1992 dissertation
%t A002537 LinearRecurrence[{0,8,0,-9},{1,1,4,11},40] (* _Harvey P. Dale_, Jul 24 2012 *)
%K A002537 nonn
%O A002537 0,3
%A A002537 _N. J. A. Sloane_
%E A002537 More terms from _James Sellers_, Sep 08 2000