A238792 Number of palindromic partitions of n such that (multiplicity of least part) = 2*(multiplicity of greatest part).

0, 0, 0, 1, 1, 1, 2, 3, 3, 5, 4, 8, 7, 12, 11, 17, 14, 24, 22, 34, 31, 47, 39, 66, 56, 85, 76, 115, 98, 158, 130, 198, 176, 260, 226, 342, 289, 432, 382, 558, 476, 716, 611, 895, 784, 1129, 975, 1430, 1229, 1775, 1551, 2211, 1914, 2756, 2385, 3394, 2964

Offset

1,7

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..57.

Example

a(10) counts these 5 partitions (written as palindromes):  181, 262, 343, 12421, 113311.

Mathematica

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

Crossrefs

Cf. A025065, A238791, A238793, A238779.

Sequence in context: A106647 A130157 A265018 * A158745 A175108 A265145

Adjacent sequences: A238789 A238790 A238791 * A238793 A238794 A238795

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved