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A238791
Number of palindromic partitions of n such that the multiplicities of the least and greatest parts are equal.
2
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
1,2
COMMENTS
Palindromic partitions are defined at A025065.
EXAMPLE
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].
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Clark Kimberling, Mar 05 2014
STATUS
approved