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A238792
Number of palindromic partitions of n such that (multiplicity of least part) = 2*(multiplicity of greatest part).
2
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
1,7
COMMENTS
Palindromic partitions are defined at A025065.
EXAMPLE
a(10) counts these 5 partitions (written as palindromes): 181, 262, 343, 12421, 113311.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 05 2014
STATUS
approved