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A290808
Number of partitions of n into distinct Pell parts (A000129).
3
1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1
OFFSET
0
COMMENTS
All terms are 0 or 1. - Robert Israel, Aug 16 2017
LINKS
FORMULA
G.f.: Product_{k>=1} (1 + x^A000129(k)).
EXAMPLE
a(8) = 1 because we have [5, 2, 1].
MAPLE
N:= 200: # to get a(0) to a(N)
Pell:= gfun:-rectoproc({a(0)=0, a(1)=1, a(n+1)=2*a(n)+a(n-1)}, a(n), remember):
G:= 1:
for k from 1 while Pell(k) <= N do G:= G*(1+x^Pell(k)) od:
seq(coeff(G, x, n), n=0..N); # Robert Israel, Aug 16 2017
MATHEMATICA
CoefficientList[Series[Product[(1 + x^Fibonacci[k, 2]), {k, 1, 15}], {x, 0, 108}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 11 2017
STATUS
approved