A117192 Number of partitions of n into distinct parts with an even rank.

1, 0, 2, 0, 2, 2, 3, 2, 4, 6, 6, 7, 8, 12, 14, 16, 18, 24, 26, 32, 38, 46, 52, 60, 70, 83, 96, 112, 128, 148, 170, 194, 224, 256, 293, 334, 380, 432, 492, 556, 630, 712, 804, 908, 1026, 1152, 1296, 1454, 1632, 1828, 2048, 2292, 2560, 2858, 3190, 3554, 3959, 4404

Offset

1,3

Links

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

Formula

a(n) = Sum(A117195(n,k)*(1 - k mod 2): 0<=k<n).

a(n) = A117194(n)+A010054(n) = A000009(n)-A117193(n) = A117193(n)+A003406(n).

Mathematica

a[n_] := Count[IntegerPartitions[n], q_ /; EvenQ[First[q] - Length[q]] && Length[q] == Length[Union[q]]];
Array[a, 60] (* Jean-François Alcover, Oct 06 2021 *)

Crossrefs

Cf. A000009, A003406, A101709, A101708, A117193, A117194, A117195.

Sequence in context: A070101 A022830 A035663 * A078729 A300236 A238158

Adjacent sequences: A117189 A117190 A117191 * A117193 A117194 A117195

Keyword

nonn

Author

Reinhard Zumkeller, Mar 03 2006

Status

approved