OFFSET
0,9
COMMENTS
The sequence b(n>=1) = 1, 0, 1, 0, 1, 1, 1, 2, 2, 4, 4, 7, ... of absolute values counts fountains of n coins that cannot be separated into two or more fountains by cutting vertically through the fountain without splitting a coin. (This separation requires that the fountain is a left-right sequence of more elementary fountains counted by b(n).) A005169(n) = Sum_{compositions n=n1+n2+n3+...} Product b(n1)*b(n2)*.... - R. J. Mathar, Aug 22 2018
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
Convolution inverse of A005169.
a(n) ~ c * d^n, where d = 1.42009048763893649946106129818306075366296460727614... and c = -0.093433697175825717154301151812109730023054876584907211486145769... - Vaclav Kotesovec, Oct 16 2017
EXAMPLE
G.f. = 1 - x - x^3 - x^5 - x^6 - x^7 - 2*x^8 - 2*x^9 - ...
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Aug 18 2017
STATUS
approved