A002213 Number of tree-like polyhexes rooted at a hexagon and containing n hexagons.

1, 1, 5, 20, 84, 354, 1540, 6704, 29610, 131745, 591049, 2669346, 12131148, 55431285, 254539897, 1174027598, 5436826110, 25269402555, 117838870833, 551192276450, 2585418254532, 12158383558066, 57313008207960

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A002212, A002214, A002215, A002216.

Formula

G.f.: x + x*U(x) + (3/2)*x*U(x)^2 + (1/2)*x*U(x^2) + (1/3)*x*U(x)^3 + (2/3)*x*U(x^3), where U(x) = (1 - 3*x - sqrt((1-x)*(1-5*x)))/(2*x).

a(n) ~ 5^(n+1/2)/(2*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 13 2013

Extensions

Edited by Emeric Deutsch, Feb 18 2004