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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
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
Sequence in context: A238545 A325343 A238495 * A094093 A240077 A237997
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 19 2014
STATUS
approved

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Last modified July 15 00:37 EDT 2024. Contains 374323 sequences. (Running on oeis4.)