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A238789 Number of palindromic partitions of n whose least part has multiplicity <= 3.

%I A238789 #4 Mar 12 2014 12:57:42
%S A238789 1,2,2,3,3,5,5,7,8,11,11,15,17,23,23,30,33,43,46,57,62,79,83,103,112,
%T A238789 139,148,180,195,236,253,304,330,396,422,501,543,644,690,810,876,1027,
%U A238789 1105,1286,1388,1614,1734,2004,2165,2496,2684,3081,3324,3808,4096
%N A238789 Number of palindromic partitions of n whose least part has multiplicity <= 3.
%C A238789 Palindromic partitions are defined at A025065.
%e A238789 a(9) counts these 8 partitions (written as palindromes):  9, 171, 252, 414, 333, 13131, 12321, 22122.
%t A238789 z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] <= k) &]
%t A238789 Table[p[n, 2], {n, 1, 12}]
%t A238789 t2 = Table[Length[p[n, 2]], {n, 1, z}]  (* A238788 *)
%t A238789 Table[p[n, 3], {n, 1, 12}]
%t A238789 t3 = Table[Length[p[n, 3]], {n, 1, z}]  (* A238789 *)
%t A238789 Table[p[n, 4], {n, 1, 12}]
%t A238789 t4 = Table[Length[p[n, 4]], {n, 1, z}]  (* A238790 *)
%t A238789 (* _Peter J. C. Moses_, Mar 03 2014 *)
%Y A238789 Cf. A025065, A238788, A238790, A238779.
%K A238789 nonn,easy
%O A238789 1,2
%A A238789 _Clark Kimberling_, Mar 05 2014