A005673 - OEIS

%I M1578 #28 Apr 22 2024 10:44:41

%S 0,0,0,0,1,2,6,11,24,42,81,138,250,419,732,1214,2073,3414,5742,9411,

%T 15664,25586,42273,68882,113202,184131,301428,489654,799273,1297118,

%U 2112774

%N F(n+1)-2^[ (n+1)/2 ] -2^[ n/2 ] +1.

%D R. K. Guy, personal communication.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. K. Guy, <a href="/A005667/a005667.pdf">Letter to N. J. A. Sloane, 1987</a>

%H 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 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-5,0,2).

%F G.f. : x^4/((1-x)(1-x-x^2)(1-2x^2)); a(n)=2a(n-1)+2a(n-2)-5a(n-3)+2a(n-4); a(n+1)=sum{k=0..n, (2^floor(k/2)-1)F(n-k)}. - _Paul Barry_, Jul 28 2004

%p A005673:=-z**4/(z-1)/(z**2+z-1)/(-1+2*z**2); [Conjectured by _Simon Plouffe_ in his 1992 dissertation.]

%t LinearRecurrence[{2,2,-5,0,2},{0,0,0,0,1},40] (* _Harvey P. Dale_, Apr 22 2024 *)

%K nonn

%O 0,6

%A _N. J. A. Sloane_.