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A067590
Number of partitions of n into odious numbers (A000069).
3
1, 1, 2, 2, 4, 4, 6, 7, 11, 12, 16, 19, 25, 29, 37, 44, 56, 64, 79, 92, 112, 130, 157, 182, 217, 250, 296, 341, 401, 461, 539, 615, 717, 817, 945, 1076, 1240, 1409, 1614, 1830, 2091, 2365, 2692, 3040, 3451, 3885, 4398, 4942, 5581, 6260, 7050, 7896, 8870, 9916
OFFSET
0,3
LINKS
N. J. A. Sloane, Transforms
FORMULA
Euler Transform of characteristic function of A000069.
MAPLE
h:= proc(n) option remember; `if`(n<1, 0,
`if`(add(i, i=Bits[Split](n))::odd, n, h(n-1)))
end:
b:= proc(n, i) option remember; `if`(n=0 or i=1, 1,
b(n, h(i-1))+b(n-i, h(min(n-i, i))))
end:
a:= n-> b(n, h(n)):
seq(a(n), n=0..100); # Alois P. Heinz, Sep 08 2019
MATHEMATICA
f[n_] := f[n] = DigitCount[n, 2][[1]] // OddQ // Boole;
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d p[d], {d, Divisors[j]}] b[n - j], {j, 1, n}]/n]; b];
a[n_] := etr[f][n];
a /@ Range[0, 100] (* Jean-François Alcover, Nov 23 2020 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Naohiro Nomoto, Jan 31 2002
EXTENSIONS
a(0) corrected by Alois P. Heinz, Sep 08 2019
STATUS
approved