A211278 a(n) = number of n-lettered words in the alphabet {1, 2, 3} with as many occurrences of the substring (consecutive subword) [1, 1] as of [2, 3].

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

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,c-1) + T(r-1,c-1) + T(r-2,c-1). 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(n-1) +2*(n+3)*a(n-2) +4*(n-3)*a(n-3) +3*(-n+2)*a(n-4)=0. - R. J. Mathar, Jun 09 2013

Crossrefs

Sequence in context: A239040 A323225 A293065 * A364625 A196154 A227235

Adjacent sequences: A211275 A211276 A211277 * A211279 A211280 A211281

Keyword

nonn

Author

N. J. A. Sloane, Apr 07 2012

Status

approved