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A145401 Number of Hamiltonian cycles in P_6 X P_n. 3
0, 1, 4, 37, 154, 1072, 5320, 32675, 175294, 1024028, 5668692, 32463802, 181971848, 1033917350, 5824476298, 32989068162, 186210666468, 1053349394128, 5950467515104, 33643541208290, 190115484271760, 1074685815276400, 6073680777522430, 34330607094625734 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

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

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..400

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 (5,14,-63,12,90,-35,-66,118,-8,-82,42,28,-4,2).

FORMULA

Recurrence: a(1) = 0,

a(2) = 1,

a(3) = 4,

a(4) = 37,

a(5) = 154,

a(6) = 1072,

a(7) = 5320,

a(8) = 32675,

a(9) = 175294,

a(10) = 1024028,

a(11) = 5668692,

a(12) = 32463802,

a(13) = 181971848,

a(14) = 1033917350, and

a(n) = 5a(n-1) +14a(n-2) -63a(n-3) +12a(n-4) +90a(n-5) -35a(n-6) -66a(n-7) +118a(n-8) -8a(n-9) -82a(n-10) +42a(n-11) +28a(n-12) -4a(n-13) +2a(n-14).

G.f.: -x^2*(x -1)*(x^11 -x^10 +3*x^9 +12*x^8 -3*x^7 -3*x^4 +21*x^3 -3*x^2 -1)/(2*x^14 -4*x^13 +28*x^12 +42*x^11 -82*x^10 -8*x^9 +118*x^8 -66*x^7- 35*x^6 +90*x^5 +12*x^4 -63*x^3 +14*x^2 +5*x -1). [Colin Barker, Aug 31 2012]

MAPLE

a:= n-> (Matrix([32675, 5320, 1072, 154, 37, 4, 1, 0, 1/2, 0, -5, -16, 51, 869/2]). Matrix(14, (i, j)-> if i=j-1 then 1 elif j=1 then [5, 14, -63, 12, 90, -35, -66, 118, -8, -82, 42, 28, -4, 2][i] else 0 fi)^n)[1, 9]: seq(a(n), n=1..30);  # Alois P. Heinz, Oct 24 2009

MATHEMATICA

a[n_] := ({32675, 5320, 1072, 154, 37, 4, 1, 0, 1/2, 0, -5, -16, 51, 869/2 }.MatrixPower[Table[If[i == j-1, 1, If[j == 1, {5, 14, -63, 12, 90, -35, -66, 118, -8, -82, 42, 28, -4, 2}[[i]], 0]], {i, 1, 14}, {j, 1, 14}], n] )[[9]]; Table[a[n], {n, 1, 30}] (* Jean-Fran├žois Alcover, Feb 14 2016, after Alois P. Heinz *)

CROSSREFS

Sequence in context: A045555 A297803 A183378 * A297745 A273684 A063418

Adjacent sequences:  A145398 A145399 A145400 * A145402 A145403 A145404

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 03 2009

EXTENSIONS

More terms from Alois P. Heinz, Oct 24 2009

STATUS

approved

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Last modified March 24 19:59 EDT 2019. Contains 321448 sequences. (Running on oeis4.)