A006479 From variance of Fibonacci search.

0, 0, 0, 1, 5, 18, 52, 134, 318, 713, 1531, 3180, 6432, 12732, 24756, 47417, 89665, 167694, 310628, 570562, 1040226, 1883953, 3391799, 6073848, 10824096, 19204536, 33936456

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

References

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

Links

• K. J. Overholt, Efficiency of the Fibonacci search method, Nordisk Tidskr. Informationsbehandling (BIT) 13 (1973), 92-96.
• 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 (4,-3,-5,5,3,-2,-1).

Crossrefs

Cf. A006478.

Programs

Maple

A006479:=z**3*(1+z+z**2)/(z-1)/(z**2+z-1)**3; # conjectured by Simon Plouffe in his 1992 dissertation

Formula

(Conjecture equivalent to Plouffe g.f.): a(n) = -3 - 2*A001629(n+2) - 3*A001629(n+1) + 2*A001628(n-1) + A020701(n+1). - R. J. Mathar, Dec 06 2010