A238781 Number of palindromic partitions of n whose least part has multiplicity 1.

1, 1, 1, 1, 2, 1, 2, 2, 3, 2, 4, 2, 6, 4, 6, 4, 10, 5, 12, 7, 16, 8, 20, 10, 27, 14, 32, 16, 44, 19, 53, 25, 69, 31, 84, 36, 108, 47, 130, 55, 167, 67, 202, 83, 252, 99, 305, 119, 380, 146, 456, 173, 564, 208, 676, 250, 826, 298, 991, 352, 1205, 424, 1435

Offset

1,5

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..63.

Example

a(11) counts these partitions (written as palindromes):  [11], [5,1,5], [4,3,4], [2,3,1,3,2].

Mathematica

z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == k) &]
Table[p[n, 1], {n, 1, 12}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A238781 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238782 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238783 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238784 *)
(* Peter J. C. Moses, Mar 03 2014 *)

Crossrefs

Cf. A025065, A238782, A238783, A238784, A238779.

Sequence in context: A283451 A172245 A351005 * A319439 A051275 A025799

Adjacent sequences: A238778 A238779 A238780 * A238782 A238783 A238784

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved