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%I #4 Mar 12 2014 12:57:35
%S 1,2,1,3,3,4,4,7,6,11,9,13,15,22,18,29,28,40,38,55,52,75,70,97,96,133,
%T 123,173,167,225,215,291,282,380,361,479,468,619,590,780,757,986,952,
%U 1239,1202,1555,1500,1931,1882,2409,2328,2975,2898,3676,3568,4517
%N Number of palindromic partitions of n whose least part has multiplicity <= 2.
%C Palindromic partitions are defined at A025065.
%e a(8) counts these 7 partitions (written as palindromes): 8, 161, 44, 242, 323, 1331, 12221
%t z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] <= k) &]
%t Table[p[n, 2], {n, 1, 12}]
%t t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238788 *)
%t Table[p[n, 3], {n, 1, 12}]
%t t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238789 *)
%t Table[p[n, 4], {n, 1, 12}]
%t t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238790 *)
%t (* _Peter J. C. Moses_, Mar 03 2014 *)
%Y Cf. A025065, A238789, A238790, A238779.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Mar 05 2014
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