The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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