A266741 -id:A266741 - cp's OEIS frontend

A266737 Number of words on {1,1,1,2,2,2,3,3,3,4,4,4,...,n,n,n} avoiding the pattern 1234.

1, 1, 20, 1680, 173891, 21347262, 2977892253, 455912368540, 74876841353159, 12990339123973119, 2354973430941967605, 442587722191655715108, 85717352536181708342445, 17029266882947116165470103, 3457866959157770598680361537, 715559803849259851987691458500

Offset: 0

N. J. A. Sloane, Jan 06 2016

nonn

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, preprint 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

Cf. A014606, A220097, A266734, A266735, A266736-A266741.

More terms from Alois P. Heinz, Jan 14 2016

A266736 Number of words on {1,1,1,2,2,2,3,3,3,4,4,4,...,n,n,n} avoiding the pattern 123.

Original entry on oeis.org

1, 1, 20, 374, 8124, 190893, 4727788, 121543500, 3212914524, 86782926068, 2384725558736, 66456350375566, 1873703883228900, 53351152389518550, 1531960347453263112, 44311785923563130392, 1289909841595078198172, 37760636720455988917420, 1110927659386926734186992

Offset: 0

N. J. A. Sloane, Jan 06 2016

nonn

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, preprint arXiv:1505.01389 [math.CO], 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
Nathaniel Shar, Experimental methods in permutation patterns and bijective proof, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.

Cf. A220097, A266734, A266735, A266737-A266741.

Conjecture: a(n) = (2/Pi)*Integral_{t=0..1} sqrt((1 - t)/t)*(64*t^3 - 32*t^2)^n = Catalan(3*n)*2F1(-1-3*n,-n;1/2-3*n;1/2). - Benedict W. J. Irwin, Oct 05 2016

More terms from Alois P. Heinz, Jan 14 2016

A266740 Number of words on {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,...,n,n,n,n} avoiding the pattern 1234.

Original entry on oeis.org

1, 1, 70, 34650, 16140983, 8854463421, 5532980565456, 3798011394008444, 2798461806432513085, 2179251644112128926809, 1774029308605731224234922, 1497612094060753803137726582, 1303178757814574200714348639251, 1163471249071555286949793002571005

Offset: 0

N. J. A. Sloane, Jan 06 2016

nonn

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, preprint 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

Cf. A220097, A266734, A266735, A266737-A266741.

More terms from Alois P. Heinz, Jan 14 2016

A266738 Number of words on {1,1,1,2,2,2,3,3,3,4,4,4,...,n,n,n} avoiding the pattern 12345.

Original entry on oeis.org

1, 1, 20, 1680, 369600, 117392909, 46121962742, 21198300356500, 11003612776114008, 6290031043253973544, 3887357166155963541538, 2562077915376091538040250, 1782153151031487742187453640, 1297781266782084301101836538690, 983066960483171632842827775906144

Offset: 0

N. J. A. Sloane, Jan 06 2016

nonn

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, preprint 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

Cf. A014606, A220097, A266734, A266735, A266736-A266741.

More terms from Alois P. Heinz, Jan 14 2016

A266739 Number of words on {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,...,n,n,n,n} avoiding the pattern 123.

Original entry on oeis.org

1, 1, 70, 3199, 173860, 10203181, 631326526, 40553993125, 2678871322640, 180830423671450, 12418980645870820, 864996624914197495, 60957211831578399100, 4338372535640598835279, 311386494956413595138930, 22513820432313175983170649, 1638226907374445245497453464

Offset: 0

N. J. A. Sloane, Jan 06 2016

nonn

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, preprint 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
Nathaniel Shar, Experimental methods in permutation patterns and bijective proof, PhD Dissertation, Mathematics Department, Rutgers University, May 2016.

Cf. A220097, A266734, A266735, A266737-A266741.

More terms from Alois P. Heinz, Jan 14 2016

cp's OEIS Frontend

A266737 Number of words on {1,1,1,2,2,2,3,3,3,4,4,4,...,n,n,n} avoiding the pattern 1234.

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A266736 Number of words on {1,1,1,2,2,2,3,3,3,4,4,4,...,n,n,n} avoiding the pattern 123.

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A266740 Number of words on {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,...,n,n,n,n} avoiding the pattern 1234.

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A266738 Number of words on {1,1,1,2,2,2,3,3,3,4,4,4,...,n,n,n} avoiding the pattern 12345.

Views

Author

Keywords

Links

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Extensions

A266739 Number of words on {1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,...,n,n,n,n} avoiding the pattern 123.

Views

Author

Keywords

Links

Crossrefs

Extensions