A002214 Number of unrooted hexagonal polyominoes with n cells and no reflections allowed. (Formerly M1750 N0694)

1, 1, 2, 7, 18, 64, 226, 856, 3306, 13249, 53794, 222717, 933438, 3960487, 16970362, 73381453, 319817670, 1403875491, 6202064928, 27559699507, 123115236582, 552654175124, 2491870281372, 11281732737898, 51270697159708, 233822055167579, 1069835253304014, 4909835353596645, 22596879316320522

Offset

1,3

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n=1..200

F. Harary and R. C. Read, The enumeration of tree-like polyhexes, Proc. Edinburgh Math. Soc. (2) 17 (1970), 1-13.

Formula

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

a(n) ~ 5^(n+1/2)/(2*sqrt(Pi)*n^(5/2)). - Vaclav Kotesovec, Aug 13 2013

Prog

(PARI) x = 'x+O('x^66);
U(x) = (1-3*x-sqrt(1-6*x+5*x^2))/(2*x);
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);
Vec(gf) \\ Joerg Arndt, Aug 13 2013

Crossrefs

Sequence in context: A176813 A000988 A185308 * A303742 A340738 A368593

Adjacent sequences: A002211 A002212 A002213 * A002215 A002216 A002217

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Emeric Deutsch, May 02 2004

Status

approved