A238791 -id:A238791 - cp's OEIS frontend

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

Clark Kimberling, Mar 05 2014

Palindromic partitions are defined at A025065.

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

Cf. A025065, A238791, A238793, A238779.

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}]

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

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

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