A104270 a(n) = 2^(n-2)*(C(n,2)+2).

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

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

M. Klazar, On identities concerning the numbers of crossings and nestings of two edges in matchings

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