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A238785 Number of palindromic partitions of n whose greatest part has multiplicity <= 2.

%I A238785 #4 Mar 12 2014 12:57:07
%S A238785 1,2,1,3,3,5,6,9,9,15,16,23,24,36,37,54,55,78,81,113,115,161,164,223,
%T A238785 228,310,315,423,430,572,582,768,778,1023,1037,1349,1368,1772,1793,
%U A238785 2309,2336,2992,3027,3856,3896,4946,4996,6305,6369,8012,8086,10129,10220
%N A238785 Number of palindromic partitions of n whose greatest part has multiplicity <= 2.
%C A238785 Palindromic partitions are defined at A025065.
%e A238785 a(6) counts these partitions (written as palindromes):  6, 141, 33, 1221, 11211.
%t A238785 z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Max[#]] <= k) &]
%t A238785 Table[p[n, 1], {n, 1, 12}]
%t A238785 t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238785 *)
%t A238785 Table[p[n, 3], {n, 1, 12}]
%t A238785 t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238786 *)
%t A238785 Table[p[n, 4], {n, 1, 12}]
%t A238785 t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238787 *)
%t A238785 (* _Peter J. C. Moses_, Mar 03 2014 *)
%Y A238785 Cf. A025065, A238786, A238787, A238779.
%K A238785 nonn,easy
%O A238785 1,2
%A A238785 _Clark Kimberling_, Mar 05 2014