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A002214 Number of unrooted hexagonal polyominoes with n cells and no reflections allowed.
(Formerly M1750 N0694)
2
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 (list; graph; refs; listen; history; text; internal format)
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 A218684 A100408

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

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Last modified October 19 16:17 EDT 2019. Contains 328223 sequences. (Running on oeis4.)