A238004 Limiting row of the array at A238325.

2, 2, 4, 4, 2, 4, 6, 4, 4, 6, 4, 4, 12, 2, 4, 4, 8, 6, 8, 4, 4, 8, 12, 4, 12, 4, 4, 8, 8, 4, 6, 18, 8, 4, 4, 8, 8, 4, 12, 12, 6, 24, 2, 4, 4, 8, 8, 4, 8, 12, 6, 12, 12, 24, 10, 4, 4, 8, 8, 4, 8, 12, 12, 8, 12, 6, 36, 4, 8, 20, 4, 4, 8, 8, 4, 8, 12, 8, 8, 12

Offset: 0

Author

Clark Kimberling and Peter J. C. Moses, Feb 25 2014

Keywords

• nonn
• easy

Comments

For fixed m >= 2 and sufficiently large k, the first m+1 antidiagonal partitions of k, listed in reverse Mathematica order, are as follows: p(0) = [1,1,...,1] (k 1's), p(1) = [2,1,...,1] (k-2 1's), p(2) = [2,2,1,...,1] (k-4 1's), ..., p[m] = [2,...,2,1,...,1] (m 2's and k-2m 1's). The number of occurrences of p(n) among all the partitions of k (for sufficiently large k), is a(n); see Example.

Examples

			Referring to the antidiagonal partitions p(i) in Comments, p(0) occurs 2 times for all k >=2; p(1) occurs 2 times for all k >=5; p(2) occurs 4 times for all k >= 7; p(3) occurs 4 times for all k >= 9; etc., so that A238004 begins with 2, 2, 4, 4.
		

Links

• Clark Kimberling and Peter J. C. Moses, Ferrers Matrices and Related Partitions of Integers

Crossrefs

Cf. A238325.

Programs

Mathematica

ferrersMatrix[list_] := PadRight[Map[Table[1, {#}] &, #], {#, #} &[Max[#, Length[#]]]] &[list]; antiDiagPartNE[list_] := Module[{m = ferrersMatrix[list]},    Map[Diagonal[Reverse[m], #] &, Range[-#, #] &[Length[m] - 1]]]; a[n_] := Last[Transpose[Tally[Map[DeleteCases[Reverse[Sort[Map[Count[#, 1] &, antiDiagPartNE[#]]]], 0] &, IntegerPartitions[n]]]]]
Take[a[40], 100] (* Peter J. C. Moses, Feb 18 2014 *)