A238006 Number of strict partitions of n such that (greatest part) - (least part) > (number of parts).

0, 0, 0, 0, 1, 1, 2, 3, 5, 6, 8, 11, 14, 18, 22, 27, 33, 41, 49, 59, 70, 83, 98, 116, 136, 159, 186, 215, 249, 289, 333, 383, 441, 505, 578, 660, 752, 856, 974, 1105, 1252, 1418, 1602, 1808, 2039, 2295, 2581, 2901, 3255, 3649, 4088, 4573, 5111, 5709, 6368

Offset

1,7

Links

Table of n, a(n) for n=1..55.

Formula

A001227(n) + A238005(n) + a(n) = A000009(n). - R. J. Mathar, Sep 08 2021

From Omar E. Pol, Sep 11 2021: (Start)

a(n) = A000009(n) - A003056(n).

a(n) = A238007(n) - A238005(n). (End)

Example

a(8) = 3 counts these partitions:  7+1, 6+2, 5+2+1.

Mathematica

z = 70; q[n_] := q[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &]; p1[p_] := p1[p] = DeleteDuplicates[p]; t[p_] := t[p] = Length[p1[p]];
Table[Count[q[n], p_ /; Max[p] - Min[p] < t[p]], {n, z}]  (* A001227 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] <= t[p]], {n, z}] (* A003056 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] == t[p]], {n, z}] (* A238005 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] > t[p]], {n, z}]  (* A238006 *)
Table[Count[q[n], p_ /; Max[p] - Min[p] >= t[p]], {n, z}] (* A238007 *)

Crossrefs

Cf. A000009, A001227, A003056, A238005, A238007.

Sequence in context: A179101 A127312 A081830 * A329289 A117517 A339732

Adjacent sequences: A238003 A238004 A238005 * A238007 A238008 A238009

Keyword

nonn,easy

Author

Clark Kimberling, Feb 17 2014

Status

approved