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

1,6

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..55.

Example

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

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 *)

Crossrefs

Cf. A025065, A087897, A238780, A114921.

Sequence in context: A100824 A163227 A325690 * A239832 A240010 A283502

Adjacent sequences: A238776 A238777 A238778 * A238780 A238781 A238782

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved