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

1,10

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..63.

Example

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

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 *)

Crossrefs

Cf. A025065, A238791, A238792, A238779.

Sequence in context: A046821 A239691 A265496 * A240677 A030306 A119348

Adjacent sequences: A238790 A238791 A238792 * A238794 A238795 A238796

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved