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 A005672 M3253 #26 Apr 13 2022 13:25:17 %S A005672 0,0,0,1,1,4,5,13,18,39,57,112,169,313,482,859,1341,2328,3669,6253, %T A005672 9922,16687,26609,44320,70929,117297,188226,309619,497845,815656, %U A005672 1313501,2145541 %N A005672 a(n) = Fibonacci(n+1) - 2^floor(n/2). %D A005672 R. K. Guy, personal communication. %D A005672 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005672 R. K. Guy, <a href="/A005667/a005667.pdf">Letter to N. J. A. Sloane, 1987</a> %H A005672 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 A005672 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992 %F A005672 a(n) = Fibonacci(n-1) + 2*a(n-2), a(-1)=0, a(1)=0, a(2)=1. - _Zerinvary Lajos_, Mar 17 2008 %p A005672 A005672:=z**3/(z**2+z-1)/(-1+2*z**2); # conjectured by _Simon Plouffe_ in his 1992 dissertation %p A005672 with (combinat):a[ -1]:=0:a[1]:=0:a[2]:=1:for n from 2 to 50 do a[n]:=fibonacci(n-1)+2*a[n-2] od: seq(a[n-1], n=0..31); # _Zerinvary Lajos_, Mar 17 2008 %Y A005672 Gives diagonal sums of triangle A054143. %K A005672 nonn,easy %O A005672 0,6 %A A005672 _N. J. A. Sloane_