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

Author

Clark Kimberling, Mar 05 2014

Keywords

• nonn
• easy

Comments

Palindromic partitions are defined at A025065.

Examples

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

Crossrefs

Cf. A025065, A238781, A238783, A238784, A238779.

Programs

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 *)