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%I #4 Mar 12 2014 12:57:50
%S 1,2,2,4,3,6,6,10,9,14,14,22,21,32,29,45,43,62,61,87,83,118,113,159,
%T 153,214,206,283,272,368,359,485,469,627,607,808,784,1036,1004,1318,
%U 1282,1670,1628,2112,2053,2651,2583,3317,3235,4134,4034,5138,5013,6355
%N Number of palindromic partitions of n whose least part has multiplicity <= 4.
%C Palindromic partitions are defined at A025065.
%e a(8) counts these 10 partitions (written as palindromes): 8, 161, 44, 242, 11411, 323, 1331, 2222, 12221, 112211.
%t z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] <= k) &]
%t Table[p[n, 2], {n, 1, 12}]
%t t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238788 *)
%t Table[p[n, 3], {n, 1, 12}]
%t t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238789 *)
%t Table[p[n, 4], {n, 1, 12}]
%t t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238790 *)
%t (* _Peter J. C. Moses_, Mar 03 2014 *)
%Y Cf. A025065, A238788, A238789, A238779.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Mar 05 2014
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