A238708 Number of strict partitions of n that include a pair of consecutive integers.

0, 0, 0, 1, 0, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 13, 15, 19, 23, 28, 33, 41, 48, 58, 68, 81, 95, 113, 131, 154, 179, 209, 241, 281, 323, 374, 429, 494, 565, 649, 739, 845, 961, 1095, 1241, 1411, 1595, 1807, 2039, 2303, 2593, 2923, 3283, 3691, 4139, 4643, 5195

Offset: 0

Author

Clark Kimberling, Mar 03 2014

Keywords

• nonn
• easy

Comments

Column 2 of the array at A238709.

Column k=1 of A238354. - Alois P. Heinz, May 02 2014

Examples

			a(10) = 4 counts these partitions: 721, 541, 532, 4321.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A238709, A000009, A238354.

Programs

Mathematica

PartitionsQ[Range[50]] - Table[Count[IntegerPartitions[n], p_ /; Min[p] >= Length[p]], {n, 50}]

Formula

a(n) = A000009(n) - A003114(n). - George Beck, Jan 01 2022