A145406 Number of Hamiltonian cycles in O_6 X P_n.

16, 1568, 105080, 7178840, 490094648, 33459179864, 2284284179000, 155949857160056, 10646817995958872, 726866542276644152, 49623743965671329432, 3387851582022139415576, 231291261492682043873912, 15790434246516135813006104, 1078025222761987287876732152, 73597620101387422536267848888

Offset

1,1

References

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

Links

Robert Israel, Table of n, a(n) for n = 1..544

F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

F. Faase, Counting Hamiltonian cycles in product graphs.

F. Faase, Results from the counting program

Index entries for linear recurrences with constant coefficients, signature (76,-542,936,2987,-9940,4896,9600,-8192).

Formula

Recurrence:

a(1) = 16,

a(2) = 1568,

a(3) = 105080,

a(4) = 7178840,

a(5) = 490094648,

a(6) = 33459179864,

a(7) = 2284284179000,

a(8) = 155949857160056,

a(9) = 10646817995958872, and

a(n) = 76a(n-1) - 542a(n-2) + 936a(n-3) + 2987a(n-4) - 9940a(n-5) + 4896a(n-6) + 9600a(n-7) - 8192a(n-8).

Maple

f:= gfun:-rectoproc({a(1) = 16,
a(2) = 1568, a(3) = 105080, a(4) = 7178840, a(5) = 490094648,
a(6) = 33459179864, a(7) = 2284284179000, a(8) = 155949857160056,
  a(9) = 10646817995958872,
a(n) = 76*a(n-1) - 542*a(n-2) + 936*a(n-3) + 2987*a(n-4) - 9940*a(n-5) + 4896*a(n-6) + 9600*a(n-7) - 8192*a(n-8)}, a(n), remember):
map(f, [$1..30]); # Robert Israel, Jul 08 2016

Mathematica

a[n_] := a[n] = If[n<10, {16, 1568, 105080, 7178840, 490094648, 33459179864, 2284284179000, 155949857160056, 10646817995958872}[[n]], 76a[n-1] - 542a[n-2] + 936a[n-3] + 2987a[n-4] - 9940a[n-5] + 4896a[n-6] + 9600a[n-7] - 8192a[n-8]];
a /@ Range[30] (* Jean-François Alcover, Aug 21 2022 *)

Crossrefs

Sequence in context: A054947 A071900 A321247 * A307924 A263387 A264199

Adjacent sequences: A145403 A145404 A145405 * A145407 A145408 A145409

Keyword

nonn,easy

Author

N. J. A. Sloane, Feb 03 2009

Status

approved