A266734 Number of words on {1,1,2,2,3,3,...,n,n} avoiding the pattern 1234.

1, 1, 6, 90, 1879, 47024, 1331664, 41250519, 1367533365, 47808569835, 1744233181074, 65905305836049, 2564220925607625, 102277575120518170, 4167486279986250932, 172988069360147449566, 7298137818882637998561, 312349784398279829229533, 13539988681466075755541070

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..580

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; Local copy, pdf file only, no active links

Formula

Conjecture: +3*n*(620202643096396011773 -608794959941727250938*n +146949290712243118000*n^2) *(n+1)^2 *(2*n+1)^2 *a(n) -n*(94389117512395618060544*n^6 -419724075420172456531120*n^5 +442263508538458916585360*n^4 +229131363207555256548194*n^3 -477880029525553894746823*n^2 +160086316440678171209939*n -11163647575735128211914) *a(n-1) -3*(n-1) *(23820522077322908587584*n^6 -1446304460086201780480376*n^5 +11080409117453774846145540*n^4 -35494287160655892321199502*n^3 +57163416479212379649118767*n^2 -45988763994280198223305139*n +14778623468656583258390502) *a(n-2) +36*(n-2) *(41902292735037258217056*n^6 -783254865433733876219472*n^5 +5235970136340811777332552*n^4 -17094365117036393449118734*n^3 +29518557363755878023892305*n^2 -25895204716899392803468055*n +9075752633781608162944050) *a(n-3) -8748*(n-2) *(125877543736438014048*n^2 -450267700517870762570*n +370949541619209268475) *(n-3)^2 *(2*n-7)^2 *a(n-4)=0. - R. J. Mathar, Apr 15 2016

Crossrefs

Cf. A220097, A266735.

Column k=3 of A267479.

Sequence in context: A006480 A138462 A002896 * A004996 A001499 A147630

Adjacent sequences: A266731 A266732 A266733 * A266735 A266736 A266737

Keyword

nonn

Author

N. J. A. Sloane, Jan 06 2016

Extensions

More terms from Alois P. Heinz, Jan 14 2016

Status

approved