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%I #4 Mar 12 2014 12:58:06
%S 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,
%T 115,98,158,130,198,176,260,226,342,289,432,382,558,476,716,611,895,
%U 784,1129,975,1430,1229,1775,1551,2211,1914,2756,2385,3394,2964
%N Number of palindromic partitions of n such that (multiplicity of least part) = 2*(multiplicity of greatest part).
%C Palindromic partitions are defined at A025065.
%e a(10) counts these 5 partitions (written as palindromes): 181, 262, 343, 12421, 113311.
%t 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}]
%t Table[Length[p[n]], {n, 1, z}]
%Y Cf. A025065, A238791, A238793, A238779.
%K nonn,easy
%O 1,7
%A _Clark Kimberling_, Mar 05 2014
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