A236292 Number of distinct cyclic permutations of the partitions of n; see comments.
1, 2, 4, 8, 16, 27, 48, 75, 118, 178, 265, 377, 544, 760, 1048, 1437, 1949, 2611, 3480, 4594, 6024, 7867, 10184, 13122, 16823, 21484, 27258, 34495, 43425, 54499, 68105, 84870, 105322, 130412, 160832, 197932, 242776, 297145, 362535, 441464, 536064, 649703
Offset: 1
Examples
a(6) = (4,2,2,2,1)*(1,2,3,4,5) = 27, where * = convolution. The 5 components of (4,2,2,2,1) count these partitions: (6, 33, 222, 1111); (51, 42); (411, 321); (3111, 2211); (211111).
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..400
Crossrefs
Cf. A236293.
Programs
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Mathematica
Map[Total[Map[Length, Map[(# /. Table[x_, {Length[#]}] -> {x}) &, IntegerPartitions[#]]]] &, Range[40]] (* A236292 *) (* Peter J. C. Moses, Jan 21 2014 *)
Formula
a(n) = (d(n), f(2), f(3),..., f(n-1))*(1,2,3,...,n-1), where d(n) = (number of divisors of n) = (number of constant partitions of n), and f(k) = number of nonconstant partitions of n, for k = 2,3,...,n-1.
Comments