A238787 Number of palindromic partitions of n whose greatest part has multiplicity <= 4.

1, 2, 2, 4, 3, 6, 6, 11, 11, 17, 18, 27, 28, 41, 42, 62, 63, 90, 91, 129, 131, 183, 185, 255, 257, 351, 354, 480, 484, 647, 652, 867, 873, 1152, 1159, 1520, 1529, 1990, 2001, 2591, 2605, 3352, 3369, 4316, 4336, 5526, 5550, 7042, 7071, 8931, 8967, 11284

Offset

1,2

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..52.

Example

a(8) counts these 11 partitions (written as palindromes):  8, 161, 44, 242, 11411, 323, 1331, 2222, 12221, 112211, 1112111.

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}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238785 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238786 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238787 *)
(* Peter J. C. Moses, Mar 03 2014 *)

Crossrefs

Cf. A025065, A238785, A238786, A238779.

Sequence in context: A341466 A357709 A238790 * A293170 A341469 A101200

Adjacent sequences: A238784 A238785 A238786 * A238788 A238789 A238790

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved