A211284 - OEIS

A211284

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

%I #8 Mar 03 2017 19:47:58

%S 1,3,9,25,70,197,554,1563,4416,12502,35463,100783,286965,818614,

%T 2339534,6698297,19211785,55197778,158857016,457932482,1322162806,

%U 3823263357,11071998176,32109724225,93248516464,271155229971,789479244108,2301369264646,6716318395056,19622420290276,57388871934035

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

%H Shalosh B. Ekhad and Doron Zeilberger, <a href="http://arxiv.org/abs/1112.6207">Automatic Solution of Richard Stanley's Amer. Math. Monthly Problem #11610 and ANY Problem of That Type</a>, arXiv preprint arXiv:1112.6207, 2011. See subpages for rigorous derivations of g.f., recurrence, asymptotics for this sequence.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Apr 07 2012