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A238779
Number of palindromic partitions of n with greatest part of multiplicity 2.
15
0, 1, 0, 1, 1, 2, 2, 4, 3, 7, 6, 11, 9, 18, 15, 27, 23, 40, 35, 59, 51, 85, 75, 119, 106, 168, 150, 231, 208, 316, 286, 428, 388, 575, 525, 764, 700, 1012, 929, 1327, 1223, 1732, 1601, 2246, 2080, 2898, 2692, 3715, 3459, 4748, 4428, 6032, 5638, 7635, 7150
OFFSET
1,6
COMMENTS
Palindromic partitions are defined at A025065.
EXAMPLE
a(8) counts these partitions (each written as a palindrome): 44, 323, 1331, 112211.
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}]
t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A000009(n-1), n>=1 *)
Table[p[n, 2], {n, 1, 12}]
t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238779 *)
Table[p[n, 3], {n, 1, 12}]
t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A087897(n-3), n>=3 *)
Table[p[n, 4], {n, 1, 12}]
t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238780 *)
(* Peter J. C. Moses, Mar 03 2014 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 05 2014
STATUS
approved