OFFSET
0,3
COMMENTS
A partition is level if the powers of 2 dividing its parts are all equal.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = Sum_{k=0..A007814(n)} A000009(n/2^k). a(2*n+1) = A000009(2*n+1) = A078408(n). - Vladeta Jovovic, Sep 29 2004
MAPLE
b:= proc(n, i, p) option remember; `if`(n=0, 1,
`if`(i<1, 0, add(b(n-i*j, i-p, p), j=0..n/i)))
end:
a:= n-> (m-> `if`(n=0, 1, add(b(n, (h-> h-1+irem(h, 2)
)(iquo(n, 2^j))*2^j, 2^(1+j)), j=0..m)))(ilog2(n)):
seq(a(n), n=0..60); # Alois P. Heinz, Jun 11 2015
MATHEMATICA
a[n_] := Sum[ PartitionsQ[n/2^k], {k, 0, IntegerExponent[n, 2]}]; Table[ a[n], {n, 1, 55}] (* Jean-François Alcover, Dec 12 2011, after Vladeta Jovovic *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Vladeta Jovovic, Mar 02 2000
EXTENSIONS
a(0)=1 prepended by Alois P. Heinz, Jun 11 2015
STATUS
approved