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A178249 Table T(n,k) counts the involutions of n with longest increasing contiguous subsequence of length k. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified August 22 20:41 EDT 2019. Contains 326196 sequences. (Running on oeis4.)