A238785 Number of palindromic partitions of n whose greatest part has multiplicity <= 2.

1, 2, 1, 3, 3, 5, 6, 9, 9, 15, 16, 23, 24, 36, 37, 54, 55, 78, 81, 113, 115, 161, 164, 223, 228, 310, 315, 423, 430, 572, 582, 768, 778, 1023, 1037, 1349, 1368, 1772, 1793, 2309, 2336, 2992, 3027, 3856, 3896, 4946, 4996, 6305, 6369, 8012, 8086, 10129, 10220

Offset

1,2

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..53.

Example

a(6) counts these partitions (written as palindromes):  6, 141, 33, 1221, 11211.

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, A238786, A238787, A238779.

Sequence in context: A034394 A058689 A173510 * A241389 A190568 A340623

Adjacent sequences: A238782 A238783 A238784 * A238786 A238787 A238788

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved