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A238004 Limiting row of the array at A238325. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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.

LINKS

Table of n, a(n) for n=0..79.

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A238325.

Sequence in context: A065176 A060267 A214516 * A048244 A056673 A128442

Adjacent sequences:  A238001 A238002 A238003 * A238005 A238006 A238007

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved

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Last modified August 4 00:29 EDT 2021. Contains 346441 sequences. (Running on oeis4.)