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A267479 Number A(n,k) of words on {1,1,2,2,...,n,n} with longest increasing subsequence of length <= k; square array A(n,k), n>=0, k>=0, read by antidiagonals. 8
1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 6, 1, 0, 1, 1, 6, 43, 1, 0, 1, 1, 6, 90, 352, 1, 0, 1, 1, 6, 90, 1879, 3114, 1, 0, 1, 1, 6, 90, 2520, 47024, 29004, 1, 0, 1, 1, 6, 90, 2520, 102011, 1331664, 280221, 1, 0, 1, 1, 6, 90, 2520, 113400, 5176504, 41250519, 2782476, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

LINKS

Alois P. Heinz, Antidiagonals n = 0..30, flattened

Ferenc Balogh, A generalization of Gessel's generating function to enumerate words with double or triple occurrences in each letter and without increasing subsequences of a given length, arXiv:1505.01389, 2015

Shalosh B. Ekhad and Doron Zeilberger, The Generating Functions Enumerating 12..d-Avoiding Words with r occurrences of each of 1,2, ..., n are D-finite for all d and all r, 2014

FORMULA

A(n,k) = Sum_{i=0..k} A267480(n,i).

EXAMPLE

Square array A(n,k) begins:

  1, 1,     1,       1,       1,       1,       1, ...

  0, 1,     1,       1,       1,       1,       1, ...

  0, 1,     6,       6,       6,       6,       6, ...

  0, 1,    43,      90,      90,      90,      90, ...

  0, 1,   352,    1879,    2520,    2520,    2520, ...

  0, 1,  3114,   47024,  102011,  113400,  113400, ...

  0, 1, 29004, 1331664, 5176504, 7235651, 7484400, ...

CROSSREFS

Columns k=0-4 give: A000007, A000012, A220097, A266734, A266735.

Main diagonal gives A000680.

First lower diagonal gives A267532.

Cf. A214015, A267480.

Sequence in context: A059117 A196603 A318458 * A285824 A269955 A198754

Adjacent sequences:  A267476 A267477 A267478 * A267480 A267481 A267482

KEYWORD

nonn,tabl,changed

AUTHOR

Alois P. Heinz, Jan 15 2016

STATUS

approved

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Last modified October 22 23:18 EDT 2018. Contains 316518 sequences. (Running on oeis4.)