A240856 Number of partitions p of n into distinct parts not including 2*(number of parts).

0, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 3, 3, 3, 4, 5, 6, 8, 10, 10, 13, 14, 17, 20, 24, 28, 33, 38, 44, 50, 58, 66, 76, 88, 100, 116, 132, 150, 170, 194, 219, 248, 280, 316, 358, 404, 453, 512, 574, 644, 723, 809, 904, 1010, 1128, 1258, 1404, 1563, 1738, 1934

Offset

0,10

Links

Table of n, a(n) for n=0..59.

Formula

a(n) + A240856(n) = A000009(n) for n >= 0.

Example

a(12) = counts these 3 partitions:  84, 651, 642.

Mathematica

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; Table[Count[f[n], p_ /; MemberQ[p, 2*Length[p]]], {n, 0, z}] (* A240856 *)

Crossrefs

Cf. A240854.

Sequence in context: A262950 A227398 A003105 * A081166 A173910 A036846

Adjacent sequences: A240853 A240854 A240855 * A240857 A240858 A240859

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved