A238792 -id:A238792 - cp's OEIS frontend

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

Clark Kimberling, Mar 05 2014

Palindromic partitions are defined at A025065.

			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].

Cf. A025065, A238792, A238793, A238779.

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}]

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

Original entry on oeis.org

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

Clark Kimberling, Mar 05 2014

Palindromic partitions are defined at A025065.

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

Cf. A025065, A238791, A238792, A238779.

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 *)

cp's OEIS Frontend

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

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