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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. 2
1, 1, 20, 374, 8124, 190893, 4727788, 121543500, 3212914524, 86782926068, 2384725558736, 66456350375566, 1873703883228900, 53351152389518550, 1531960347453263112, 44311785923563130392, 1289909841595078198172, 37760636720455988917420, 1110927659386926734186992 (list; graph; refs; listen; history; text; internal format)
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: A290581 A000564 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

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Last modified July 16 23:49 EDT 2019. Contains 325092 sequences. (Running on oeis4.)