A116492 Number of partitions of n into distinct odious numbers.

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5, 6, 7, 8, 10, 11, 11, 12, 14, 16, 17, 19, 20, 21, 23, 27, 30, 32, 36, 38, 41, 45, 50, 54, 58, 64, 68, 74, 80, 88, 95, 102, 111, 119, 128, 138, 149, 160, 172, 186, 200, 214, 230, 248, 266, 285, 308, 327, 348, 373, 400, 429

Offset

0,8

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 1001 terms from Andrew Howroyd)

N. J. A. Sloane, Transforms

Formula

Weigh Transform of characteristic function of A000069.

Maple

g:= proc(n) option remember; is(add(i, i=Bits[Split](n))::odd) end:
b:= proc(n, i) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, 1,
      b(n, i-1)+`if`(g(i), b(n-i, min(n-i, i-1)), 0)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..100);  # Alois P. Heinz, Sep 08 2019

Mathematica

seq[n_] := Product[If[OddQ[Total[DigitCount[Abs[k], 2, 1]]], 1 + x^k, 1], {k, 1, n}] + O[x]^n // CoefficientList[#, x]&;
seq[100] (* Jean-François Alcover, Sep 08 2019 *)

Prog

(PARI) seq(n)={Vec(prod(k=1, n, if(hammingweight(k)%2==1, 1+x^k, 1) + O(x*x^n)))} \\ Andrew Howroyd, Jun 22 2018

Crossrefs

Cf. A067590, A116491.

Sequence in context: A194316 A261796 A200245 * A103263 A173777 A140436

Adjacent sequences: A116489 A116490 A116491 * A116493 A116494 A116495

Keyword

nonn

Author

Christian G. Bower, Feb 17 2006

Status

approved