A238779 - OEIS

%I #8 Mar 17 2014 01:26:44

%S 0,1,0,1,1,2,2,4,3,7,6,11,9,18,15,27,23,40,35,59,51,85,75,119,106,168,

%T 150,231,208,316,286,428,388,575,525,764,700,1012,929,1327,1223,1732,

%U 1601,2246,2080,2898,2692,3715,3459,4748,4428,6032,5638,7635,7150

%N Number of palindromic partitions of n with greatest part of multiplicity 2.

%C Palindromic partitions are defined at A025065.

%e a(8) counts these partitions (each written as a palindrome):  44, 323, 1331, 112211.

%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 t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A000009(n-1), n>=1 *)

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

%t t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238779 *)

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

%t t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A087897(n-3), n>=3 *)

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

%t t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238780 *)

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

%Y Cf. A025065, A087897, A238780, A114921.

%K nonn,easy

%O 1,6

%A _Clark Kimberling_, Mar 05 2014