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%I #24 Oct 08 2018 06:12:36
%S 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,
%T 48,49,51,54,55,58,59,62,64,65,66,76,77,78,80,83,84,87,88,89,90,94,95,
%U 96,97,100,101,104,106,107,108,123,124,125,127,130,131,134,135,136,137,141,142
%N Exponents in g.f. Product_{k>=2} (1 - x^{F_k}) where F_k are the Fibonacci numbers.
%H F. Ardila, <a href="http://arXiv.org/abs/math.CO/0409418">The Coefficients of a Fibonacci power series</a>, arXiv:math/0409418 [math.CO], 2004.
%H N. Robbins, <a href="http://www.fq.math.ca/Scanned/34-4/robbins.pdf">Fibonacci Partitions</a>, The Fibonacci Quarterly, 34.4 (1996), pp. 306-313.
%H Yufei Zhao, <a href="http://www.fq.math.ca/Papers1/46_47-1/Zhao_12-08.pdf">The coefficients of a truncated Fibonacci power series</a>, Fib. Q., 46/47 (2008/2009), 53-55.
%e 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 - ...
%t 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 *)
%Y Cf. A000045, A093996.
%K nonn
%O 1,3
%A _N. J. A. Sloane_, May 30 2009
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