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A238708
Number of strict partitions of n that include a pair of consecutive integers.
3
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
0,8
COMMENTS
Column 2 of the array at A238709.
Column k=1 of A238354. - Alois P. Heinz, May 02 2014
LINKS
FORMULA
a(n) = A000009(n) - A003114(n). - George Beck, Jan 01 2022
EXAMPLE
a(10) = 4 counts these partitions: 721, 541, 532, 4321.
MATHEMATICA
PartitionsQ[Range[50]] - Table[Count[IntegerPartitions[n], p_ /; Min[p] >= Length[p]], {n, 50}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 03 2014
STATUS
approved