A238791 Number of palindromic partitions of n such that the multiplicities of the least and greatest parts are equal.

1, 2, 2, 3, 2, 5, 2, 5, 3, 7, 2, 11, 3, 10, 6, 15, 5, 22, 7, 28, 12, 33, 15, 52, 21, 59, 33, 84, 38, 112, 56, 145, 77, 178, 103, 251, 132, 300, 184, 404, 229, 507, 304, 645, 398, 800, 506, 1040, 639, 1270, 832, 1608, 1032, 1988, 1310, 2479, 1640, 3031, 2053

Offset

1,2

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..59.

Example

a(10) counts these 7 partitions (written as palindromes):  [10], [5,5], [1,4,4,1], [2,3,3,2], [1,3,2,3,1], [2,2,2,2,2], 1,1,1,1,1,1,1,1,1,1].

Mathematica

z = 40; p[n_] := p[n] = Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == Count[#, Max[#]]) &]; Table[p[n], {n, 1, 12}]
Table[Length[p[n]], {n, 1, z}]

Crossrefs

Cf. A025065, A238792, A238793, A238779.

Sequence in context: A326843 A323347 A322900 * A007012 A343371 A298423

Adjacent sequences: A238788 A238789 A238790 * A238792 A238793 A238794

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved