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 A104270 a(n) = 2^(n-2)*(C(n,2)+2). 3
 1, 3, 10, 32, 96, 272, 736, 1920, 4864, 12032, 29184, 69632, 163840, 380928, 876544, 1998848, 4521984, 10158080, 22675456, 50331648, 111149056, 244318208, 534773760, 1166016512, 2533359616, 5486149632, 11844714496 (list; graph; refs; listen; history; text; internal format)
 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 Equals (1/2) A053730. Partial sums of A084264. Sequence in context: A286444 A080406 A036682 * A038731 A244762 A053581 Adjacent sequences:  A104267 A104268 A104269 * A104271 A104272 A104273 KEYWORD nonn,easy AUTHOR Ralf Stephan, Apr 17 2005 STATUS approved

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Last modified March 28 13:21 EDT 2020. Contains 333089 sequences. (Running on oeis4.)