A238493 Number of partitions p of n such that max(p) - min(p) is a part of p.

0, 0, 1, 1, 2, 4, 4, 7, 10, 14, 15, 27, 28, 43, 50, 69, 80, 115, 127, 176, 204, 268, 310, 412, 471, 606, 710, 892, 1042, 1311, 1517, 1885, 2203, 2692, 3146, 3834, 4459, 5392, 6293, 7540, 8781, 10494, 12186, 14482, 16832, 19874, 23066, 27171, 31445, 36893

Offset

1,5

Links

Table of n, a(n) for n=1..50.

Formula

a(n) + A238494(n) = A000041(n).

Example

a(6) = 4 counts these partitions:  42, 321, 2211, 21111.

Mathematica

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Max[p] - Min[p]]], {n, 50}]

Crossrefs

Cf. A238494.

Sequence in context: A284612 A070072 A265259 * A362937 A268781 A282647

Adjacent sequences: A238490 A238491 A238492 * A238494 A238495 A238496

Keyword

nonn,easy

Author

Clark Kimberling, Feb 27 2014

Status

approved