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A093996 G.f.: Product_{k>=2} (1 - x^{F_k}) where F_k are the Fibonacci numbers. 5
1, -1, -1, 0, 1, 0, 0, 1, -1, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 0, 1, 1, -1, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, 1, 0, -1, -1, 1, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, -1, 0, 1, 1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 1, 0, 0, 1, -1, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, -1, 1, 0, 0, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Number of partitions of n with an even number of distinct Fibonacci parts minus the number of partitions of n with an odd number of distinct Fibonacci parts.

Every term is -1, 0 or 1.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

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

Neville 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.

FORMULA

Ardila gives a fast recurrence.

a(n) = A093998(n) - A093997(n).

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 - ... - N. J. A. Sloane, May 30 2009

MATHEMATICA

Take[ CoefficientList[ Expand[ Product[1 - x^Fibonacci[k], {k, 2, 13}]], x], 105] (* Robert G. Wilson v, May 29 2004 *)

nn = 11; Take[CoefficientList[Expand[Product[1 - x^Fibonacci[n], {n, 2, nn}]], x], Fibonacci[nn+1]] (* T. D. Noe, Feb 27 2014 *)

CROSSREFS

Cf. A000045, A000119, A093997, A093998, A151661.

Sequence in context: A192687 A189141 A082416 * A323095 A336868 A083187

Adjacent sequences:  A093993 A093994 A093995 * A093997 A093998 A093999

KEYWORD

easy,sign

AUTHOR

N. Sato, May 24 2004

EXTENSIONS

Edited and extended by Robert G. Wilson v, May 29 2004

STATUS

approved

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Last modified September 19 03:31 EDT 2021. Contains 347550 sequences. (Running on oeis4.)