OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = a(n-1) + Sum_{k>=0} a(n-(1+2^k)), with a(-1) = a(0) = 1 and a(n) = 0 for n < -1.
G.f.: (1 + h(x))/(1 - x - x*h(x)) where h(x) = sum(k >= 0, x^(2^k)) is the g.f. of A209229. - Robert Israel, Jan 04 2015
EXAMPLE
For n = 4, the a(4) = 14 solutions are 0000, 0001, 0010, 0100, 1000, 0101, 1001, 1010, 0011, 0110, 1100, 1011, 1101, and 1111.
MAPLE
a:= proc(n) option remember; `if`(n<1, 1,
a(n-1) +add(a(n-1-2^k), k=0..ilog2(n)))
end:
seq(a(n), n=0..50); # Alois P. Heinz, Jan 03 2015
MATHEMATICA
terms = 35; h[x_] = Sum[x^2^k, {k, 0, Log[2, terms] // Floor}];
CoefficientList[(1 + h[x])/(1 - x - x h[x]) + O[x]^terms, x] (* Jean-François Alcover, Mar 22 2019, after Robert Israel *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Woods, Jan 02 2015
STATUS
approved