A238788 Number of palindromic partitions of n whose least part has multiplicity <= 2.

1, 2, 1, 3, 3, 4, 4, 7, 6, 11, 9, 13, 15, 22, 18, 29, 28, 40, 38, 55, 52, 75, 70, 97, 96, 133, 123, 173, 167, 225, 215, 291, 282, 380, 361, 479, 468, 619, 590, 780, 757, 986, 952, 1239, 1202, 1555, 1500, 1931, 1882, 2409, 2328, 2975, 2898, 3676, 3568, 4517

Offset

1,2

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..56.

Example

a(8) counts these 7 partitions (written as palindromes):  8, 161, 44, 242, 323, 1331, 12221

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, A238789, A238790, A238779.

Sequence in context: A339396 A027157 A112194 * A350844 A083041 A318611

Adjacent sequences: A238785 A238786 A238787 * A238789 A238790 A238791

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved