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A212802 Row 5 of array in A212801. 2
1, 121, 5611, 193721, 6050000, 183990301, 5598183221, 171567260161, 5290933752571, 163756656800000, 5076226921767101, 157423577321804321, 4881873153941565211, 151371085451034210421, 4692977668021522550000, 145487069742178319930401 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths 5 and n. - Andrew Howroyd, Jan 12 2018

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Germain Kreweras, Complexité et circuits Eulériens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212.

FORMULA

From Andrew Howroyd, Jan 12 2018: (Start)

Empirical: a(n) = 121*a(n-1) - 6520*a(n-2) + 209330*a(n-3) - 4493120*a(n-4) + 68446433*a(n-5) - 766303183*a(n-6) + 6438802040*a(n-7) - 41070618160*a(n-8) + 199602863240*a(n-9) - 736417358863*a(n-10) + 2039087685503*a(n-11) - 4149490675520*a(n-12) + 5992940178830*a(n-13) - 5786524000120*a(n-14) + 3329026307431*a(n-15) - 852891037441*a(n-16) for n > 16.

Empirical g.f.: x*(1 - 31*x^2)*(1 - 2479*x^2 + 94380*x^3 - 1719180*x^4 + 18597458*x^5 - 128373600*x^6 + 576521198*x^7 - 1652131980*x^8 + 2811674580*x^9 - 2289408559*x^10 + 887503681*x^12)/((1 - x)*(1 - 31*x)*(1 - 12*x + 31*x^2)*(1 - 9*x + 31*x^2 - 49*x^3 + 31*x^4)*(1 - 19*x + 151*x^2 - 589*x^3 + 961*x^4)*(1 - 49*x + 961*x^2 - 8649*x^3 + 29791*x^4)).

(End)

MATHEMATICA

T[m_, n_] := Product[2 - Exp[2*I*h*Pi/m] - Exp[2*I*k*Pi/n], {h, 1, m - 1}, {k, 1, n - 1}];

a[n_] := T[5, n] // Round;

Array[a, 20] (* Jean-François Alcover, Jul 04 2018 *)

CROSSREFS

Cf. A212801.

Sequence in context: A069600 A244065 A231649 * A272775 A018849 A011814

Adjacent sequences:  A212799 A212800 A212801 * A212803 A212804 A212805

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 27 2012

STATUS

approved

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Last modified May 18 03:03 EDT 2021. Contains 343994 sequences. (Running on oeis4.)