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

1,2

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.

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 *)

Crossrefs

Main diagonal of A212801.

Cf. A054759, A297385.

Sequence in context: A269187 A185702 A279046 * A002109 A259373 A076265

Adjacent sequences: A212800 A212801 A212802 * A212804 A212805 A212806

Keyword

nonn

Author

N. J. A. Sloane, May 27 2012

Extensions

Name clarified by Andrew Howroyd, Jan 12 2018

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

Status

approved