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 A093998 Number of partitions of n with an even number of distinct Fibonacci parts. 4
 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 1, 2, 1, 2, 1, 0, 2, 2, 2, 2, 1, 2, 2, 1, 3, 1, 1, 2, 1, 2, 2, 2, 3, 1, 2, 3, 1, 3, 2, 2, 3, 1, 3, 2, 1, 3, 2, 2, 2, 1, 2, 2, 2, 4, 1, 3, 3, 1, 4, 3, 3, 3, 1, 3, 3, 2, 4, 2, 3, 3, 1, 4, 2, 2, 4, 2, 3, 3, 2, 3, 2, 2, 3, 0, 2, 3, 2, 4, 2, 4, 3, 1, 5, 3, 3, 4, 2, 4, 4, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10946 F. Ardila, The coefficients of a Fibonacci power series, Fib. Quart. 42 (3) (2004), 202-204. N. Robbins, Fibonacci partitions, Fib. Quart. 34 (4) (1996), 306-313. J. Shallit, Robbins and Ardila meet Berstel, Arxiv preprint arXiv:2007.14930 [math.CO], 2020. FORMULA G.f.: (Product_{k>=2} (1 + x^{F_k}) + Product_{k>=2} (1 - x^{F_k}))/2. MAPLE F:= combinat[fibonacci]: b:= proc(n, i, t) option remember; `if`(n=0, t, `if`(i<2, 0,        b(n, i-1, t)+`if`(F(i)>n, 0, b(n-F(i), i-1, 1-t))))     end: a:= proc(n) local j; for j from ilog[(1+sqrt(5))/2](n+1)        while F(j+1)<=n do od; b(n, j, 1)     end: seq(a(n), n=0..100);  # Alois P. Heinz, Jul 11 2013 MATHEMATICA Take[ CoefficientList[ Expand[ Product[1 + x^Fibonacci[k], {k, 2, 13}]/2 + Product[1 - x^Fibonacci[k], {k, 2, 13}]/2], x], 105] (* Robert G. Wilson v, May 29 2004 *) CROSSREFS Cf. A000119, A093997. Sequence in context: A225089 A262436 A336499 * A247918 A237203 A339444 Adjacent sequences:  A093995 A093996 A093997 * A093999 A094000 A094001 KEYWORD easy,nonn 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 July 25 13:05 EDT 2021. Contains 346290 sequences. (Running on oeis4.)