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

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

Offset

0,3

Links

Table of n, a(n) for n=0..18.

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.

Formula

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

Crossrefs

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

Sequence in context: A000564 A365415 A178352 * A019580 A177109 A162806

Adjacent sequences: A266733 A266734 A266735 * A266737 A266738 A266739

Keyword

nonn

Author

N. J. A. Sloane, Jan 06 2016

Extensions

More terms from Alois P. Heinz, Jan 14 2016

Status

approved