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