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A239329 The number of NE partitions of n (see Comments). 1
1, 2, 3, 4, 7, 9, 14, 19, 27, 36, 51, 67, 90, 117, 157, 204, 266, 337, 436, 554, 708, 890, 1123, 1401, 1750, 2172, 2701, 3329, 4106, 5026, 6161, 7507, 9147, 11095, 13455, 16245, 19597, 23555, 28288, 33867, 40514, 48328, 57590, 68456, 81286, 96286, 113947 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Directional partitions are defined at A237981, and NE partitions are shown at A237982.  a(n) is also the number of SW partitions of n, as at A237982.

LINKS

Table of n, a(n) for n=1..47.

EXAMPLE

                                            (* See A237982 *)

MATHEMATICA

z = 9; 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 A237981*)

Flatten[Map[cP[[#, 2]] &, Range[Length[cP]]]]; (*NE A237982*)

Flatten[Map[cP[[#, 3]] &, Range[Length[cP]]]]; (*SE A237983*)

Flatten[Map[cP[[#, 4]] &, Range[Length[cP]]]]; (*SW A237982*)

m1 = Map[cP[[#, 1]] &, Range[Length[cP]]];

Table[Length[m1[[k]]], {k, 1, z}] (* A003114, NW *)

m2 = Map[cP[[#, 2]] &, Range[Length[cP]]];

Table[Length[m2[[k]]], {k, 1, z}] (* A239329, NE *)

m3 = Map[cP[[#, 3]] &, Range[Length[cP]]];

Table[Length[m3[[k]]], {k, 1, z}] (* A122129, SE *)

m4 = Map[cP[[#, 4]] &, Range[Length[cP]]];

Table[Length[m4[[k]]], {k, 1, z}] (* A239329, SW *)

CROSSREFS

Cf. A003114, A122129, A237981, A237982.

Sequence in context: A238545 A325343 A238495 * A094093 A240077 A237997

Adjacent sequences:  A239326 A239327 A239328 * A239330 A239331 A239332

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Mar 19 2014

STATUS

approved

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Last modified May 16 10:04 EDT 2022. Contains 353700 sequences. (Running on oeis4.)