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A317239
Number of partitions of n into distinct parts with an even sum of Hamming weights.
2
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
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
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jul 24 2018
STATUS
approved