

A174469


Number of permutations p of {1,...,n} satisfying p(1)=1 and, if n>1, p(i)p((i mod n)+1) is in {2,3} for i from 1 to n.


1



1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 2, 4, 6, 8, 10, 12, 16, 22, 30, 40, 52, 68, 90, 120, 160, 212, 280, 370, 490, 650, 862, 1142, 1512, 2002, 2652, 3514, 4656, 6168, 8170, 10822, 14336, 18992, 25160, 33330, 44152, 58488, 77480, 102640, 135970
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OFFSET

1,5


COMMENTS

Also the number of directed Hamiltonian cycles in the graph on n vertices {1,...,n}, with i adjacent to j iff 2 <= ij <= 3.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..1000
Weisstein, Eric W. "Hamiltonian Cycle".


FORMULA

G.f.: (3*x^52*x^4+x1)*x / (x^5+x1).
a(n) = 2*A017899(n5) for n>=5.


EXAMPLE

For n = 10 the a(10) = 2 permutations are (1,3,6,9,7,10,8,5,2,4), (1,4,2,5,8,10,7,9,6,3).


MAPLE

a:= n> `if` (n<2, n, (Matrix (5, (i, j)> `if` (ji=1 or i=5 and j in {1, 5}, 1, 0))^n. <<2, 2, (0$3)>>)[1, 1]): seq (a(n), n=1..60);


CROSSREFS

Cf. A017899.
Sequence in context: A028961 A110177 A036273 * A112166 A112167 A230571
Adjacent sequences: A174466 A174467 A174468 * A174470 A174471 A174472


KEYWORD

nonn


AUTHOR

Alois P. Heinz, Nov 28 2010


STATUS

approved



