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%I M1750 N0694 #27 Dec 29 2016 02:28:38
%S 1,1,2,7,18,64,226,856,3306,13249,53794,222717,933438,3960487,
%T 16970362,73381453,319817670,1403875491,6202064928,27559699507,
%U 123115236582,552654175124,2491870281372,11281732737898,51270697159708,233822055167579,1069835253304014,4909835353596645,22596879316320522
%N Number of unrooted hexagonal polyominoes with n cells and no reflections allowed.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A002214/b002214.txt">Table of n, a(n) for n=1..200</a>
%H F. Harary and R. C. Read, <a href="https://doi.org/10.1017/S0013091500009135">The enumeration of tree-like polyhexes</a>, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.
%F G.f.: x + x*U(x) + (1/2)*(3*x-1)*U(x)^2 + (1/2)*(1+x)*U(x^2) + (1/3)*x*U(x)^3 + (2/3)*x*U(x^3), where U(x)=(1-3*x-sqrt(1-6*x+5*x^2))/(2*x). - _Emeric Deutsch_, May 02 2004
%F a(n) ~ 5^(n+1/2)/(2*sqrt(Pi)*n^(5/2)). - _Vaclav Kotesovec_, Aug 13 2013
%o (PARI) x = 'x+O('x^66);
%o U(x) = (1-3*x-sqrt(1-6*x+5*x^2))/(2*x);
%o gf = x + x*U(x) + (1/2)*(3*x-1)*U(x)^2 + (1/2)*(1+x)*U(x^2) + (1/3)*x*U(x)^3 + (2/3)*x*U(x^3);
%o Vec(gf) \\ _Joerg Arndt_, Aug 13 2013
%K nonn
%O 1,3
%A _N. J. A. Sloane_
%E More terms from _Emeric Deutsch_, May 02 2004
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