|
Search: id:A003435
|
|
|
| A003435 |
|
Number of Hamiltonian circuits on n-octahedron.
(Formerly M4578)
|
|
+0
2
|
|
| 8, 192, 11904, 1125120, 153262080, 28507207680, 6951513784320, 2153151603671040, 826060810479206400, 384600188992919961600, 213656089636192754073600, 139620366072628402087526400, 106033731334825319789808844800
(list; graph; listen)
|
|
|
OFFSET
|
2,1
|
|
|
COMMENT
|
Also called the relaxed menage problem (cf. A000179).
These are labeled and the order and starting point matter.
|
|
REFERENCES
|
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Bogart, Kenneth P. and Doyle, Peter G., Nonsexist solution of the menage problem, Amer. Math. Monthly 93 (1986), no. 7, 514-519.
Singmaster, David, Hamiltonian circuits on the n-dimensional octahedron. J. Combinatorial Theory Ser. B 19 (1975), no. 1, 1-4.
|
|
FORMULA
|
For n >= 2, a(n) = sum((-1)^k*binomial(n, k)*((2*n)/(2*n-k))*2^k*(2*n-k)!, k=0..n).
|
|
EXAMPLE
|
n=2: label vertices of a square 1,2,3,4. Then the 8 Hamiltonian circuits are 1234, 1432, 2341, 2143, 3412, 3214, 4123, 4321; so a(2) = 8.
|
|
MAPLE
|
A003435 := n->add((-1)^k*binomial(n, k)*((2*n)/(2*n-k))*2^k*(2*n-k)!, k=0..n);
|
|
CROSSREFS
|
Cf. A003436, A003437.
Sequence in context: A129004 A058873 A052734 this_sequence A071303 A128406 A003956
Adjacent sequences: A003432 A003433 A003434 this_sequence A003436 A003437 A003438
|
|
KEYWORD
|
nonn,nice,easy
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
