A117193 - OEIS

A117193

Number of partitions of n into distinct parts with an odd rank.

0, 1, 0, 2, 1, 2, 2, 4, 4, 4, 6, 8, 10, 10, 13, 16, 20, 22, 28, 32, 38, 43, 52, 62, 72, 82, 96, 110, 128, 148, 170, 196, 224, 256, 292, 334, 380, 432, 490, 557, 630, 714, 806, 908, 1022, 1152, 1294, 1456, 1632, 1830, 2049, 2290, 2560, 2860, 3188, 3554, 3958, 4404

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OFFSET

1,4

LINKS

Table of n, a(n) for n=1..58.

FORMULA

a(n) = Sum(A117195(n,k)*(k mod 2): 0<=k<n).

a(n) = A000009(n) - A117192(n).

a(n) = A117192(n) - A003406(n).

MATHEMATICA

a[n_] := Count[IntegerPartitions[n], q_ /; OddQ[First[q] - Length[q]] && Length[q] == Length[Union[q]]];

Array[a, 60] (* Jean-François Alcover, Oct 06 2021 *)