A005673 F(n+1)-2^[ (n+1)/2 ] -2^[ n/2 ] +1. (Formerly M1578)

0, 0, 0, 0, 1, 2, 6, 11, 24, 42, 81, 138, 250, 419, 732, 1214, 2073, 3414, 5742, 9411, 15664, 25586, 42273, 68882, 113202, 184131, 301428, 489654, 799273, 1297118, 2112774

Offset

0,6

References

R. K. Guy, personal communication.

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

Links

Table of n, a(n) for n=0..30.

R. K. Guy, Letter to N. J. A. Sloane, 1987

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.

Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992

Index entries for linear recurrences with constant coefficients, signature (2,2,-5,0,2).

Formula

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

Maple

A005673:=-z**4/(z-1)/(z**2+z-1)/(-1+2*z**2); [Conjectured by Simon Plouffe in his 1992 dissertation.]

Mathematica

LinearRecurrence[{2, 2, -5, 0, 2}, {0, 0, 0, 0, 1}, 40] (* Harvey P. Dale, Apr 22 2024 *)

Crossrefs

Sequence in context: A102429 A080012 A103143 * A084308 A067605 A072986

Adjacent sequences: A005670 A005671 A005672 * A005674 A005675 A005676

Keyword

nonn

Author

N. J. A. Sloane.

Status

approved