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

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 *)

Crossrefs

Cf. A000009, A003406, A101707, A117192.

Sequence in context: A204596 A324387 A163373 * A325707 A026832 A225044

Adjacent sequences: A117190 A117191 A117192 * A117194 A117195 A117196

Keyword

nonn

Author

Reinhard Zumkeller, Mar 03 2006

Status

approved