A151661 Exponents in g.f. Product_{k>=2} (1 - x^{F_k}) where F_k are the Fibonacci numbers.

0, 1, 2, 4, 7, 8, 11, 12, 13, 14, 18, 19, 20, 22, 23, 24, 29, 30, 31, 33, 36, 38, 39, 40, 47, 48, 49, 51, 54, 55, 58, 59, 62, 64, 65, 66, 76, 77, 78, 80, 83, 84, 87, 88, 89, 90, 94, 95, 96, 97, 100, 101, 104, 106, 107, 108, 123, 124, 125, 127, 130, 131, 134, 135, 136, 137, 141, 142

Offset

1,3

Links

Table of n, a(n) for n=1..68.

F. Ardila, The Coefficients of a Fibonacci power series, arXiv:math/0409418 [math.CO], 2004.

N. Robbins, Fibonacci Partitions, The Fibonacci Quarterly, 34.4 (1996), pp. 306-313.

Yufei Zhao, The coefficients of a truncated Fibonacci power series, Fib. Q., 46/47 (2008/2009), 53-55.

Example

1 - x - x^2 + x^4 + x^7 - x^8 + x^11 - x^12 - x^13 + x^14 + x^18 - x^19 - x^20 + x^22 + x^23 - x^24 + x^29 - x^30 - x^31 + x^33 + x^36 - x^38 - x^39 + x^40 + x^47 - ...

Mathematica

kmax = 150; Exponent[#, x]& /@ List @@ (Product[1 - x^Fibonacci[k], {k, 2, Ceiling[FindRoot[Fibonacci[x] == kmax, {x, 5}][[1, 2]]]}] + O[x]^kmax // Normal) (* Jean-François Alcover, Oct 08 2018 *)

Crossrefs

Cf. A000045, A093996.

Sequence in context: A093701 A045601 A167051 * A094599 A050082 A209864

Adjacent sequences: A151658 A151659 A151660 * A151662 A151663 A151664

Keyword

nonn

Author

N. J. A. Sloane, May 30 2009

Status

approved