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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
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
Sequence in context: A194316 A261796 A200245 * A103263 A173777 A140436
KEYWORD
nonn
AUTHOR
Christian G. Bower, Feb 17 2006
STATUS
approved