A290808 Number of partitions of n into distinct Pell parts (A000129).

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

Robert Israel, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Pell Number

Index entries for sequences related to partitions

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

Cf. A000119, A000121, A000129, A003263, A290807.

Sequence in context: A328308 A257196 A176137 * A364252 A190239 A120529

Adjacent sequences: A290805 A290806 A290807 * A290809 A290810 A290811

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 11 2017

Status

approved