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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. 7
1, 3, 21, 2862, 5398083, 105918450471, 18761832172500795, 29912416165371498901002, 429210477536602279123636967061, 55428311030379722725246681652572022523 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..9.

FORMULA

(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 and (1/8)*(3^(n^2)+2*3^(n^2/4)+3*3^(n^2/2)+2*3^((n^2+n)/2)) if n is odd.

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

Cf. A054247.

Sequence in context: A290872 A012110 A265637 * A117508 A001139 A277628

Adjacent sequences:  A054736 A054737 A054738 * A054740 A054741 A054742

KEYWORD

easy,nonn

AUTHOR

Vladeta Jovovic, May 15 2000

STATUS

approved

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Last modified November 19 00:12 EST 2019. Contains 329310 sequences. (Running on oeis4.)