A211305 - OEIS

A211305

a(n) = number of n-lettered words in the alphabet {1, 2, 3, 4} with as many occurrences of the substring (consecutive subword) [1, 1] as of [2, 3].

%I #12 Oct 23 2017 15:02:41

%S 1,4,14,49,173,617,2222,8076,29605,109384,407059,1524662,5743964,

%T 21751969,82752733,316107245,1211853152,4660656826,17974865576,

%U 69496877137,269292154210,1045525145898,4066354568134,15840022855209,61789766045683,241338711779257,943701096216542,3693967024612846

%N a(n) = number of n-lettered words in the alphabet {1, 2, 3, 4} with as many occurrences of the substring (consecutive subword) [1, 1] as of [2, 3].

%H Alois P. Heinz, <a href="/A211305/b211305.txt">Table of n, a(n) for n = 0..1000</a>

%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 08 2012