A240858 Number of partitions p of n into distinct parts not including max(p) - min(p).

0, 1, 1, 1, 2, 3, 2, 5, 5, 6, 7, 12, 11, 16, 16, 23, 27, 33, 35, 47, 52, 65, 75, 88, 101, 121, 139, 164, 190, 219, 249, 294, 334, 384, 443, 504, 577, 659, 746, 851, 971, 1097, 1242, 1409, 1585, 1790, 2023, 2271, 2557, 2873, 3221, 3612, 4049, 4521, 5054, 5651

Offset

0,5

Links

Table of n, a(n) for n=0..55.

Formula

a(n) + A240852(n) = A000009(n) for n >= 0.

Example

a(10) counts all 10 partitions of 10 into distinct parts except for 541, 532, 4321, so that a(10) = 7.

Mathematica

z = 40; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; Table[Count[f[n], p_ /; MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A240852 *)
    Table[Count[f[n], p_ /; !MemberQ[p, Max[p] - Min[p]]], {n, 0, z}] (* A240858 *)

Crossrefs

Cf. A240852, A000009.

Sequence in context: A144307 A144310 A330049 * A035361 A137851 A369742

Adjacent sequences: A240855 A240856 A240857 * A240859 A240860 A240861

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved