A212803 Number of Eulerian circuits in the Cartesian product of two directed cycles of lengths n.

1, 4, 108, 12800, 6050000, 11218701312, 81959473720768, 2376692369090150400, 275204089028043534645504, 127722545775271195902771200000, 238045190395699755964859156456705024, 1783083199654005767436422099232872202240000, 53684915729010675246823790713834564866472376291328

Offset: 1

Author

N. J. A. Sloane, May 27 2012

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• Germain Kreweras, Complexité et circuits Eulériens dans les sommes tensorielles de graphes, J. Combin. Theory, B 24 (1978), 202-212.

Crossrefs

Main diagonal of A212801.

Cf. A054759, A297385.

Programs

Mathematica

a[n_] := Product[2-E^(2 h Pi I/n)-E^(2 k Pi I/n), {h, 1, n-1}, {k, 1, n-1}];
Array[a, 12] // Round (* Jean-François Alcover, Sep 02 2019 *)

Extensions

Name clarified by Andrew Howroyd, Jan 12 2018

Terms a(13) and beyond from Andrew Howroyd, May 19 2020