A238782 - OEIS

%I #4 Mar 12 2014 12:56:39

%S 0,1,0,2,1,3,2,5,3,9,5,11,9,18,12,25,18,35,26,48,36,67,50,87,69,119,

%T 91,157,123,206,162,266,213,349,277,443,360,572,460,725,590,919,750,

%U 1156,950,1456,1195,1812,1502,2263,1872,2802,2334,3468,2892,4267,3574

%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 partitions (written as palindromes):  161, 44, 422, 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, 1], {n, 1, 12}]

%t t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A238781 *)

%t Table[p[n, 2], {n, 1, 12}]

%t t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238782 *)

%t Table[p[n, 3], {n, 1, 12}]

%t t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238783 *)

%t Table[p[n, 4], {n, 1, 12}]

%t t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238784 *)

%t (* _Peter J. C. Moses_, Mar 03 2014 *)

%Y Cf. A025065, A238781, A238783, A238784, A238779.

%K nonn,easy

%O 1,4

%A _Clark Kimberling_, Mar 05 2014