

A211278


a(n) = number of nlettered words in the alphabet {1, 2, 3} with as many occurrences of the substring (consecutive subword) [1, 1] as of [2, 3].


1



1, 3, 7, 16, 38, 95, 248, 668, 1838, 5131, 14470, 41112, 117475, 337203, 971515, 2807744, 8136090, 23630215, 68768210, 200481036, 585381973, 1711647959, 5011157073, 14687848012, 43095321203, 126565380735, 372030471493, 1094437253428, 3221999290418, 9492019319771, 27981390048004
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OFFSET

0,2


COMMENTS

Define a triangle by T(n,n)=n+1 and T(n,0)=1 for n>=0, and T(r,c) = T(r,c1) + T(r1,c1) + T(r2,c1). The sum of the terms in row n is a(n).  J. M. Bergot, Mar 01 2013


LINKS

Table of n, a(n) for n=0..30.
Shalosh B. Ekhad and Doron Zeilberger, Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type, arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence.


FORMULA

Conjecture: n*a(n) 4*n*a(n1) +2*(n+3)*a(n2) +4*(n3)*a(n3) +3*(n+2)*a(n4)=0.  R. J. Mathar, Jun 09 2013


CROSSREFS

Sequence in context: A239040 A323225 A293065 * A196154 A227235 A304937
Adjacent sequences: A211275 A211276 A211277 * A211279 A211280 A211281


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 07 2012


STATUS

approved



