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 A054739 Number of inequivalent n X n matrices over GF(3) under action of dihedral group of the square D_4. 9
 1, 3, 21, 2862, 5398083, 105918450471, 18761832172500795, 29912416165371498901002, 429210477536602279123636967061, 55428311030379722725246681652572022523, 64422190091501416379601522735200323789074174081, 673878862467911703904942451533575765568815772023224550102 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 0..25 FORMULA a(n) = (1/8)*(3^(n^2) + 2*3^(n^2/4) + 3*3^(n^2/2) + 2*3^((n^2+n)/2)) if n is even; a(n) = (1/8)*(3^(n^2) + 2*3^((n^2+3)/4) + 3^((n^2+1)/2) + 4*3^((n^2+n)/2)) if n is odd. [corrected by Chris Hallstrom, Mar 22 2021] MATHEMATICA Join[{1, 3}, Table[CycleIndexPolynomial[ GraphData[{"Grid", {n, n}}, "AutomorphismGroup"], Table[Subscript[s, i], {i, 1, 4}]] /. Table[Subscript[s, i] -> 3, {i, 1, 4}], {n, 2, 10}]] (* Geoffrey Critzer, Aug 09 2016 *) CROSSREFS Column k=3 of A343097. Cf. A054247. Sequence in context: A290872 A012110 A265637 * A117508 A331897 A001139 Adjacent sequences: A054736 A054737 A054738 * A054740 A054741 A054742 KEYWORD easy,nonn AUTHOR Vladeta Jovovic, May 15 2000 EXTENSIONS Terms a(10) and beyond from Andrew Howroyd, Apr 15 2021 STATUS approved

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Last modified June 6 22:19 EDT 2023. Contains 363151 sequences. (Running on oeis4.)