|
%I #26 Sep 08 2022 08:45:17
%S 1,3,10,32,96,272,736,1920,4864,12032,29184,69632,163840,380928,
%T 876544,1998848,4521984,10158080,22675456,50331648,111149056,
%U 244318208,534773760,1166016512,2533359616,5486149632,11844714496
%N a(n) = 2^(n-2)*(C(n,2)+2).
%C Cardinality of set of crossing-similarity classes.
%C Total number of hexagonal systems with n hexagons. - _Parthasarathy Nambi_, Sep 06 2006
%C 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
%H Vincenzo Librandi, <a href="/A104270/b104270.txt">Table of n, a(n) for n = 1..237</a>
%H M. Klazar, <a href="http://arXiv.org/abs/math.CO/0503012">On identities concerning the numbers of crossings and nestings of two edges in matchings</a>
%H Tosic R., Masulovic D., Stojmenovic I., Brunvoll J., Cyvin B. N. and Cyvin S. J., <a href="http://dx.doi.org/10.1021/ci00024a002">Enumeration of polyhex hydrocarbons to h = 17</a>, J. Chem. Inf. Comput. Sci., 1995, 35, 181-187, Table 1 (with an error at h=16).
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-12,8).
%F G.f.: x*(1 - 3*x + 4*x^2)/(1-2*x)^3. - _Colin Barker_, Apr 01 2012
%t Table[n!*Det[Array[KroneckerDelta[#1,#2](((#1+2)/(#1))-1)+1 &, {n,n}]], {n, 1, 10}] (* _John M. Campbell_, May 20 2011 *)
%t LinearRecurrence[{6,-12,8},{1,3,10},30] (* _Harvey P. Dale_, Jul 03 2017 *)
%o (Magma) [2^(n-2)*(Binomial(n,2)+2): n in [1..30]]; // _Vincenzo Librandi_, May 24 2011
%o (PARI) a(n)=(binomial(n,2)+2)<<(n-2) \\ _Charles R Greathouse IV_, May 24 2011
%Y Equals (1/2) A053730. Partial sums of A084264.
%K nonn,easy
%O 1,2
%A _Ralf Stephan_, Apr 17 2005
|
