OFFSET
1,2
COMMENTS
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Mar 19 2014
STATUS
approved