OFFSET
1,2
COMMENTS
Cardinality of set of crossing-similarity classes.
Total number of hexagonal systems with n hexagons. - Parthasarathy Nambi, Sep 06 2006
a(n+1) is equal to n! times the determinant of the n X n matrix whose (i,j)-entry is KroneckerDelta[i,j](((i+2)/(i)) - 1) + 1. - John M. Campbell, May 20 2011
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..237
Tosic R., Masulovic D., Stojmenovic I., Brunvoll J., Cyvin B. N. and Cyvin S. J., Enumeration of polyhex hydrocarbons to h = 17, J. Chem. Inf. Comput. Sci., 1995, 35, 181-187, Table 1 (with an error at h=16).
Index entries for linear recurrences with constant coefficients, signature (6,-12,8).
FORMULA
G.f.: x*(1 - 3*x + 4*x^2)/(1-2*x)^3. - Colin Barker, Apr 01 2012
MATHEMATICA
Table[n!*Det[Array[KroneckerDelta[#1, #2](((#1+2)/(#1))-1)+1 &, {n, n}]], {n, 1, 10}] (* John M. Campbell, May 20 2011 *)
LinearRecurrence[{6, -12, 8}, {1, 3, 10}, 30] (* Harvey P. Dale, Jul 03 2017 *)
PROG
(Magma) [2^(n-2)*(Binomial(n, 2)+2): n in [1..30]]; // Vincenzo Librandi, May 24 2011
(PARI) a(n)=(binomial(n, 2)+2)<<(n-2) \\ Charles R Greathouse IV, May 24 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Apr 17 2005
STATUS
approved