A005672 a(n) = Fibonacci(n+1) - 2^floor(n/2). (Formerly M3253)

0, 0, 0, 1, 1, 4, 5, 13, 18, 39, 57, 112, 169, 313, 482, 859, 1341, 2328, 3669, 6253, 9922, 16687, 26609, 44320, 70929, 117297, 188226, 309619, 497845, 815656, 1313501, 2145541

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..31.

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

Formula

a(n) = Fibonacci(n-1) + 2*a(n-2), a(-1)=0, a(1)=0, a(2)=1. - Zerinvary Lajos, Mar 17 2008

Maple

A005672:=z**3/(z**2+z-1)/(-1+2*z**2); # conjectured by Simon Plouffe in his 1992 dissertation
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

Crossrefs

Gives diagonal sums of triangle A054143.

Sequence in context: A234254 A258281 A094029 * A147001 A247325 A140683

Adjacent sequences: A005669 A005670 A005671 * A005673 A005674 A005675

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved