A116491 Number of partitions of n into distinct evil numbers.

1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 2, 4, 1, 3, 5, 2, 5, 5, 3, 7, 7, 5, 8, 10, 7, 11, 13, 8, 16, 17, 12, 20, 20, 17, 26, 26, 22, 31, 34, 30, 40, 43, 37, 51, 54, 48, 64, 66, 62, 80, 83, 78, 98, 103, 98, 121, 128, 122, 150, 158, 149, 184, 193, 185, 226, 233, 228, 275, 285, 280

Offset

0,10

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Transforms

Formula

Weigh Transform of characteristic function of A001969.

Maple

g:= proc(n) option remember; is(add(i, i=Bits[Split](n))::even) 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

m = 100;
Product[If[EvenQ[DigitCount[k, 2, 1]], 1 + x^k, 1], {k, 1, m}] + O[x]^m // CoefficientList[#, x]& (* Jean-François Alcover, Sep 11 2019, from PARI *)

Prog

(PARI) seq(n)=Vec(prod(k=1, n, if(hammingweight(k)%2==0, 1+x^k, 1) + O(x*x^n))) \\ Andrew Howroyd, Jun 22 2018

Crossrefs

Cf. A067591, A116492.

Sequence in context: A337511 A261363 A341216 * A131325 A193749 A049824

Adjacent sequences: A116488 A116489 A116490 * A116492 A116493 A116494

Keyword

nonn

Author

Christian G. Bower, Feb 17 2006

Status

approved