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 A237982 Triangular array read by rows: row n gives the NE partitions of n (see Comments). 5
 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 4, 3, 1, 2, 1, 1, 1, 1, 1, 1, 5, 4, 1, 3, 2, 3, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 1, 4, 2, 4, 1, 1, 3, 2, 1, 3, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 6, 1, 5, 2, 5, 1, 1, 4, 3, 4, 2, 1, 4, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See Comments at A237981 for definitions of the directional partitions, NW, NE, SW, SE. The number of NE partitions of n, and also the number of SW partitions of n, is A237329(n), for n >=1. The order is: each partition has nonincreasing parts and the partitions are ordered anti-lexicographic (called "Mathematica order" in the example). - Wolfdieter Lang, Mar 21 2014 LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 Clark Kimberling and Peter J. C. Moses, Ferrers Matrices and Related Partitions of Integers EXAMPLE The first 4 rows of the array of NW partitions: 1 2 .. 1 .. 1 3 .. 2 .. 1 .. 1 .. 1 .. 1 4 .. 3 .. 1 .. 2 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1 Row 4, for example, represents the 4 NE partitions of 4 as follows:  [4], [3,1], [2,1,1], [1,1,1,1], listed in "Mathematica order". MATHEMATICA z = 10; ferrersMatrix[list_] := PadRight[Map[Table[1, {#}] &, #], {#, #} &[Max[#, Length[#]]]] &[list]; cornerPart[list_] := Module[{f = ferrersMatrix[list], u, l, ur, lr, nw, ne, se, sw}, {u, l} = {UpperTriangularize[#, 1], LowerTriangularize[#]} &[f]; {ur, lr} = {UpperTriangularize[#, 1], LowerTriangularize[#]} &[Reverse[f]]; {nw, ne, se, sw} = {Total[Transpose[u]] + Total[l], Total[ur] + Total[Transpose[lr]], Total[u] + Total[Transpose[l]], Total[Transpose[ur]] + Total[lr]};    Map[DeleteCases[Reverse[Sort[#]], 0] &, {nw, ne, se, sw}]]; cornerParts[n_] :=  Map[#[[Reverse[Ordering[PadRight[#]]]]] &, Map[DeleteDuplicates[#] &,    Transpose[Map[cornerPart, IntegerPartitions[n]]]]]; cP = Map[cornerParts, Range[z]]; Flatten[Map[cP[[#, 1]] &, Range[Length[cP]]]](*NW corner: A237981*) Flatten[Map[cP[[#, 2]] &, Range[Length[cP]]]](*NE corner: A237982*) Flatten[Map[cP[[#, 3]] &, Range[Length[cP]]]](*SE corner: A237983*) Flatten[Map[cP[[#, 4]] &, Range[Length[cP]]]](*SW corner: A237982*) (* Peter J. C. Moses, Feb 25 2014 *) CROSSREFS Cf. A237981, A237329, A237983, A237985, A238325, A238326. Sequence in context: A277648 A026792 A139100 * A239512 A036037 A181317 Adjacent sequences:  A237979 A237980 A237981 * A237983 A237984 A237985 KEYWORD nonn,tabf,easy AUTHOR Clark Kimberling and Peter J. C. Moses, Feb 23 2014 STATUS approved

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Last modified June 15 17:43 EDT 2019. Contains 324142 sequences. (Running on oeis4.)