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A174469
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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.
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1
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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
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1,5
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COMMENTS
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Also the number of directed Hamiltonian cycles in the graph on n vertices {1,...,n}, with i adjacent to j iff 2 <= |i-j| <= 3.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..1000
Weisstein, Eric W. "Hamiltonian Cycle".
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FORMULA
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G.f.: (3*x^5-2*x^4+x-1)*x / (x^5+x-1).
a(n) = 2*A017899(n-5) for n>=5.
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EXAMPLE
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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).
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MAPLE
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a:= n-> `if` (n<2, n, (Matrix (5, (i, j)-> `if` (j-i=1 or i=5 and j in {1, 5}, 1, 0))^n. <<2, -2, (0$3)>>)[1, 1]): seq (a(n), n=1..60);
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CROSSREFS
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Cf. A017899.
Sequence in context: A028961 A110177 A036273 * A112166 A112167 A037213
Adjacent sequences: A174466 A174467 A174468 * A174470 A174471 A174472
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KEYWORD
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nonn
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AUTHOR
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Alois P. Heinz, Nov 28 2010
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STATUS
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approved
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