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%I #4 Mar 12 2014 12:57:28
%S 1,2,2,4,3,6,6,11,11,17,18,27,28,41,42,62,63,90,91,129,131,183,185,
%T 255,257,351,354,480,484,647,652,867,873,1152,1159,1520,1529,1990,
%U 2001,2591,2605,3352,3369,4316,4336,5526,5550,7042,7071,8931,8967,11284
%N Number of palindromic partitions of n whose greatest part has multiplicity <= 4.
%C Palindromic partitions are defined at A025065.
%e a(8) counts these 11 partitions (written as palindromes): 8, 161, 44, 242, 11411, 323, 1331, 2222, 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, A238786, A238779.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Mar 05 2014
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