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A238786 Number of palindromic partitions of n whose greatest part has multiplicity <= 3.

%I A238786 #4 Mar 12 2014 12:57:18
%S A238786 1,2,2,3,3,6,6,10,10,16,17,25,26,38,40,57,59,83,86,119,123,169,174,
%T A238786 235,241,325,333,443,453,599,612,802,818,1067,1087,1407,1432,1845,
%U A238786 1876,2401,2440,3110,3158,4003,4062,5130,5202,6537,6625,8298,8406,10483
%N A238786 Number of palindromic partitions of n whose greatest part has multiplicity <= 3.
%C A238786 Palindromic partitions are defined at A025065.
%e A238786 a(8) counts these 10 partitions (written as palindromes):  8, 161, 44, 242, 11411, 323, 1331, 12221, 112211, 1112111.
%t A238786 z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Max[#]] <= k) &]
%t A238786 Table[p[n, 1], {n, 1, 12}]
%t A238786 t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238785 *)
%t A238786 Table[p[n, 3], {n, 1, 12}]
%t A238786 t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238786 *)
%t A238786 Table[p[n, 4], {n, 1, 12}]
%t A238786 t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238787 *)
%t A238786 (* _Peter J. C. Moses_, Mar 03 2014 *)
%Y A238786 Cf. A025065, A238785, A238787, A238779.
%K A238786 nonn,easy
%O A238786 1,2
%A A238786 _Clark Kimberling_, Mar 05 2014