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A116492 Number of partitions of n into distinct odious numbers. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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,changed

AUTHOR

Christian G. Bower, Feb 17 2006

STATUS

approved

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Last modified September 20 03:55 EDT 2019. Contains 327212 sequences. (Running on oeis4.)