A104270 a(n) = 2^(n - 2)*(binomial(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, 25501368320, 54760833024, 117306294272, 250718715904

Offset: 1

Author

Ralf Stephan, Apr 17 2005

Keywords

• nonn
• easy

Comments

Cardinality of set of crossing-similarity classes.

Total number of hexagonal systems with n hexagons that cannot be placed in a cage of size n-1. - 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).

Crossrefs

Equals (1/2) A053730. Partial sums of A084264.

Programs

Magma

[2^(n-2)*(Binomial(n,2)+2): n in [1..30]]; // Vincenzo Librandi, May 24 2011

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 *)

PARI

a(n)=(binomial(n,2)+2)<<(n-2) \\ Charles R Greathouse IV, May 24 2011

Formula

G.f.: x*(1 - 3*x + 4*x^2)/(1-2*x)^3. - Colin Barker, Apr 01 2012