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

Author

Reinhard Zumkeller, Mar 03 2006

Keywords

• nonn

Crossrefs

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

Programs

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 *)

Formula

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

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

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