

A182027


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


1



1, 2, 2, 2, 4, 6, 12, 20, 40, 70, 140, 252, 504, 924, 1848, 3432, 6864, 12870, 25740, 48620, 97240, 184756, 369512, 705432, 1410864, 2704156, 5408312, 10400600, 20801200, 40116600, 80233200, 155117520, 310235040, 601080390, 1202160780, 2333606220, 4667212440, 9075135300, 18150270600, 35345263800
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OFFSET

0,2


LINKS

Table of n, a(n) for n=0..39.
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. [From N. J. A. Sloane, Apr 07 2012]


FORMULA

G.f.: 1 + x + x*sqrt((1+2*x)/(12*x))= 1 + x + x/G(0), where G(k)= 1  2*x/(1 + 2*x/(1 + 1/G(k+1) )); (continued fraction).  Sergei N. Gladkovskii, Jul 26 2013


CROSSREFS

Apart from initial terms, same as A063886.
Sequence in context: A000799 A185030 A063823 * A005865 A176051 A245257
Adjacent sequences: A182024 A182025 A182026 * A182028 A182029 A182030


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 07 2012


STATUS

approved



