A317239 Number of partitions of n into distinct parts with an even sum of Hamming weights.

1, 0, 0, 2, 0, 2, 3, 0, 4, 6, 3, 6, 9, 6, 12, 19, 9, 19, 31, 17, 37, 44, 29, 62, 68, 55, 91, 104, 92, 140, 162, 134, 217, 245, 207, 329, 343, 323, 489, 497, 489, 686, 726, 731, 980, 1040, 1036, 1400, 1477, 1491, 1970, 2038, 2139, 2744, 2835, 3016, 3752, 3939

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..10000

Formula

a(n) + A316996(n) = A000009(n).

a(n) ~ exp(Pi*sqrt(n/3)) / (8 * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Oct 09 2018

Maple

h:= proc(n) option remember; `if`(n=0, 0, irem(n, 2, 'q')+h(q)) end:
b:= proc(n, i, t) option remember; `if`(i*(i+1)/2<n, 0, `if`(n=0, t,
      b(n, i-1, t)+b(n-i, min(n-i, i-1), irem(t+h(i), 2))))
    end:
a:= n-> b(n$2, 1):
seq(a(n), n=0..100);

Mathematica

h[n_] := h[n] = If[n == 0, 0, Mod[n, 2] + h[Quotient[n, 2]]];
b[n_, i_, t_] := b[n, i, t] = If[i(i+1)/2 < n, 0, If[n == 0, t, b[n, i - 1, t] + b[n - i, Min[n - i, i - 1], Mod[t + h[i], 2]]]];
a[n_] := b[n, n, 1];
a /@ Range[0, 100](* Jean-François Alcover, Dec 12 2020, after Alois P. Heinz *)

Crossrefs

Cf. A000009, A000120, A316996.

Sequence in context: A181871 A269591 A262878 * A360174 A089596 A319876

Adjacent sequences: A317236 A317237 A317238 * A317240 A317241 A317242

Keyword

nonn

Author

Alois P. Heinz, Jul 24 2018

Status

approved