A240852 Number of partitions p of n into distinct parts including max(p) - min(p).

0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 3, 0, 4, 2, 6, 4, 5, 5, 11, 7, 12, 11, 14, 16, 21, 21, 26, 28, 32, 37, 47, 46, 56, 64, 69, 81, 91, 101, 118, 131, 142, 163, 184, 201, 231, 258, 281, 319, 353, 391, 437, 485, 533, 599, 664, 727, 809, 894, 979, 1091, 1201, 1316

Offset

0,7

Links

Table of n, a(n) for n=0..61.

Formula

a(n) + A240850(n) = A000009(n) for n >= 0.

Example

a(10) counts these 3 partitions:  541, 532, 4321.

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. A240858, A000009.

Sequence in context: A350369 A117398 A295989 * A363612 A309816 A071486

Adjacent sequences: A240849 A240850 A240851 * A240853 A240854 A240855

Keyword

nonn,easy

Author

Clark Kimberling, Apr 14 2014

Status

approved