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 A005673 M1578 #41 Jul 09 2025 10:52:15
%S A005673 0,0,0,0,1,2,6,11,24,42,81,138,250,419,732,1214,2073,3414,5742,9411,
%T A005673 15664,25586,42273,68882,113202,184131,301428,489654,799273,1297118,
%U A005673 2112774,3426275,5571816,9030858,14668209,23764602,38563882,62459555,101285580,164007278
%N A005673 a(n) = F(n+2) - 2^[ (n+1)/2 ] - 2^[ n/2 ] + 1.
%D A005673 R. K. Guy, personal communication.
%D A005673 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005673 R. K. Guy, <a href="/A005667/a005667.pdf">Letter to N. J. A. Sloane, 1987</a>
%H A005673 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 A005673 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A005673 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-5,0,2).
%F A005673 G.f.: x^4/((1-x)*(1-x-x^2)*(1-2x^2)); a(n) = 2*a(n-1)+2*a(n-2)-5*a(n-3)+2*a(n-5); a(n+1) = Sum_{k=0..n} (2^floor(k/2)-1)*F(n-k). - _Paul Barry_, Jul 28 2004
%p A005673 A005673:=-z**4/(z-1)/(z**2+z-1)/(-1+2*z**2); # Conjectured by _Simon Plouffe_ in his 1992 dissertation.
%t A005673 LinearRecurrence[{2,2,-5,0,2},{0,0,0,0,1},40] (* _Harvey P. Dale_, Apr 22 2024 *)
%Y A005673 Cf. A000045.
%K A005673 nonn,easy
%O A005673 0,6
%A A005673 _N. J. A. Sloane_