A238782 Number of palindromic partitions of n whose least part has multiplicity 2.

0, 1, 0, 2, 1, 3, 2, 5, 3, 9, 5, 11, 9, 18, 12, 25, 18, 35, 26, 48, 36, 67, 50, 87, 69, 119, 91, 157, 123, 206, 162, 266, 213, 349, 277, 443, 360, 572, 460, 725, 590, 919, 750, 1156, 950, 1456, 1195, 1812, 1502, 2263, 1872, 2802, 2334, 3468, 2892, 4267, 3574

Offset

1,4

Comments

Palindromic partitions are defined at A025065.

Links

Table of n, a(n) for n=1..57.

Example

a(8) counts these partitions (written as palindromes):  161, 44, 422, 1331, 12221.

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, A238781, A238783, A238784, A238779.

Sequence in context: A272912 A123231 A246995 * A058736 A097451 A005916

Adjacent sequences: A238779 A238780 A238781 * A238783 A238784 A238785

Keyword

nonn,easy

Author

Clark Kimberling, Mar 05 2014

Status

approved