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

Author

N. J. A. Sloane, May 30 2009

Keywords

• nonn

Examples

			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 - ...
		

Links

• 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.

Crossrefs

Cf. A000045, A093996.

Programs

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 *)