A238785 - OEIS

%I #4 Mar 12 2014 12:57:07

%S 1,2,1,3,3,5,6,9,9,15,16,23,24,36,37,54,55,78,81,113,115,161,164,223,

%T 228,310,315,423,430,572,582,768,778,1023,1037,1349,1368,1772,1793,

%U 2309,2336,2992,3027,3856,3896,4946,4996,6305,6369,8012,8086,10129,10220

%N Number of palindromic partitions of n whose greatest part has multiplicity <= 2.

%C Palindromic partitions are defined at A025065.

%e a(6) counts these partitions (written as palindromes):  6, 141, 33, 1221, 11211.

%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, A238786, A238787, A238779.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Mar 05 2014