A238789 Number of palindromic partitions of n whose least part has multiplicity <= 3.

1, 2, 2, 3, 3, 5, 5, 7, 8, 11, 11, 15, 17, 23, 23, 30, 33, 43, 46, 57, 62, 79, 83, 103, 112, 139, 148, 180, 195, 236, 253, 304, 330, 396, 422, 501, 543, 644, 690, 810, 876, 1027, 1105, 1286, 1388, 1614, 1734, 2004, 2165, 2496, 2684, 3081, 3324, 3808, 4096

Offset

1,2

Comments

Palindromic partitions are defined at A025065.

Links

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

Example

a(9) counts these 8 partitions (written as palindromes):  9, 171, 252, 414, 333, 13131, 12321, 22122.

Mathematica

z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] <= k) &]
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}]  (* A238788 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}]  (* A238789 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}]  (* A238790 *)
(* Peter J. C. Moses, Mar 03 2014 *)

Crossrefs

Cf. A025065, A238788, A238790, A238779.

Sequence in context: A025147 A364613 A032230 * A126793 A069910 A026797

Adjacent sequences: A238786 A238787 A238788 * A238790 A238791 A238792

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved