A238779 Number of palindromic partitions of n with greatest part of multiplicity 2.

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, 150, 231, 208, 316, 286, 428, 388, 575, 525, 764, 700, 1012, 929, 1327, 1223, 1732, 1601, 2246, 2080, 2898, 2692, 3715, 3459, 4748, 4428, 6032, 5638, 7635, 7150

Offset: 1

Author

Clark Kimberling, Mar 05 2014

Keywords

• nonn
• easy

Comments

Palindromic partitions are defined at A025065.

Examples

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

Crossrefs

Cf. A025065, A087897, A238780, A114921.

Programs

Mathematica

z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Max[#]] == k) &]
Table[p[n, 1], {n, 1, 12}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A000009(n-1), n>=1 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238779 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A087897(n-3), n>=3 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238780 *)
(* Peter J. C. Moses, Mar 03 2014 *)