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URL: https://oeis.org/A104270

⇱ A104270 - OEIS

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A104270
a(n) = 2^(n - 2)*(binomial(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, 25501368320, 54760833024, 117306294272, 250718715904
OFFSET
1,2
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
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).
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
KEYWORD
nonn,easy
AUTHOR
Ralf Stephan, Apr 17 2005
STATUS
approved