A178249 Table T(n,k) counts the involutions of n with longest increasing contiguous subsequence of length k.

1, 1, 1, 1, 2, 1, 1, 6, 2, 1, 1, 14, 8, 2, 1, 1, 37, 27, 8, 2, 1, 1, 96, 94, 30, 8, 2, 1, 1, 270, 338, 114, 30, 8, 2, 1, 1, 777, 1237, 446, 118, 30, 8, 2, 1, 1, 2370, 4684, 1809, 473, 118, 30, 8, 2, 1, 1, 7450, 18142, 7502, 1964, 478, 118, 30, 8, 2, 1, 1, 24485, 72524, 32093, 8414, 1998, 478, 118, 30, 8, 2, 1

Offset

1,5

Comments

Reverse of rows converges to 1,2,8,30,118,478,2004,8666,..

Links

Table of n, a(n) for n=1..78.

Example

T(4,2) = 6 because the 6 involutions with longest increasing contiguous subsequence lengths equal to 2 are: 1324, 1432, 2143, 3214, 3412, 4231.
Table starts:
1;
1,   1;
1,   2,   1;
1,   6,   2,   1;
1,  14,   8,   2,  1;
1,  37,  27,   8,  2, 1;
1,  96,  94,  30,  8, 2, 1;
1, 270, 338, 114, 30, 8, 2, 1;

Mathematica

(* first do *)
Needs["Combinatorica`"]
(* then *)
maxISS[perm_List] := Max[0, (Max @@ (Length[#1]*Sign[First[#1]] & ) /@ Split[Sign[Rest[#1] - Drop[#1, -1]]] & )[perm]]; classMaxISS[par_?PartitionQ]:=Count[ maxISS/@( TableauxToPermutation[FirstLexicographicTableau[par], #]&/@Tableaux[par]  ) , #]&/@(-1+Range[ Tr[par] ]);
Table[Apply[Plus, classMaxISS/@Partitions[n]], {n, 2, 6}];

Crossrefs

Cf. A008304; row sums are A000085; A047884 removes the contiguity requirement.

Sequence in context: A265315 A179380 A107106 * A119502 A142156 A136707

Adjacent sequences: A178246 A178247 A178248 * A178250 A178251 A178252

Keyword

nonn,tabl

Author

Wouter Meeussen, Dec 20 2010

Extensions

Definition corrected by Wouter Meeussen, Dec 22 2010

Status

approved