%I #12 Mar 03 2017 19:45:32

%S 1,3,7,18,47,123,328,886,2419,6675,18587,52164,147404,418991,1197002,

%T 3434568,9891715,28580469,82808899,240511642,700024987,2041255981,

%U 5962023006,17439034426,51075928264,149767494573,439619556301,1291671623988,3798447661874,11179106282223,32925086562548

%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] as of [1, 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.

%F Conjecture: n*a(n) +2*(-3*n+1)*a(n-1) +(7*n+6)*a(n-2) +2*(7*n-37)*a(n-3) +3*(-7*n+40)*a(n-4) +6*(-n-4)*a(n-5) +27*(-n+6)*a(n-6) +54*(n-6)*a(n-7)=0. - _R. J. Mathar_, May 31 2014

%K nonn

%O 0,2

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