A238786 Number of palindromic partitions of n whose greatest part has multiplicity <= 3.

1, 2, 2, 3, 3, 6, 6, 10, 10, 16, 17, 25, 26, 38, 40, 57, 59, 83, 86, 119, 123, 169, 174, 235, 241, 325, 333, 443, 453, 599, 612, 802, 818, 1067, 1087, 1407, 1432, 1845, 1876, 2401, 2440, 3110, 3158, 4003, 4062, 5130, 5202, 6537, 6625, 8298, 8406, 10483

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 10 partitions (written as palindromes):  8, 161, 44, 242, 11411, 323, 1331, 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, A238787, A238779.

Sequence in context: A116932 A240579 A292225 * A238547 A325681 A116450

Adjacent sequences: A238783 A238784 A238785 * A238787 A238788 A238789

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved