A238793 Number of palindromic partitions of n such that 2*(multiplicity of least part) = (multiplicity of greatest part).

0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 3, 1, 3, 3, 6, 5, 6, 5, 9, 9, 13, 10, 17, 13, 23, 18, 29, 23, 37, 32, 48, 37, 64, 48, 81, 60, 99, 77, 130, 94, 158, 123, 200, 145, 252, 182, 309, 224, 381, 277, 475, 331, 575, 414, 712, 497, 866, 605, 1049, 736, 1274, 883, 1555

Offset: 1

Author

Clark Kimberling, Mar 05 2014

Keywords

• nonn
• easy

Comments

Palindromic partitions are defined at A025065.

Examples

			a(15) counts these 6 partitions (written as palindromes):  717, 636, 25152, 13431, 12233221..
		

Crossrefs

Cf. A025065, A238791, A238792, A238779.

Programs

Mathematica

z = 65; p[n_] := p[n] = Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (2*Count[#, Min[#]] == Count[#, Max[#]]) &]; Table[p[n], {n, 1, 16}]
t1 = Table[Length[p[n]], {n, 1, z}]
(* Peter J. C. Moses, Mar 03 2014 *)