A286397 - OEIS

%I #38 Apr 15 2021 17:02:05

%S 1,10,1540,125512750,1250002537502500,1250000000501250002500000,

%T 125000000000000250375000000250000000,

%U 1250000000000000000005001250000000002500000000000

%N Number of inequivalent n X n matrices over an alphabet of size 10 under action of dihedral group of the square D_4.

%C Burnside's orbit-counting lemma.

%H María Merino, <a href="/A286397/b286397.txt">Table of n, a(n) for n = 0..20</a>

%H M. Merino and I. Unanue, <a href="https://doi.org/10.1387/ekaia.17851">Counting squared grid patterns with Pólya Theory</a>, EKAIA, 34 (2018), 289-316 (in Basque).

%F a(n) = (1/8)*(10^(n^2) + 2*10^(n^2/4) + 3*10^(n^2/2) + 2*10^((n^2 + n)/2)) if n is even;

%F a(n) = (1/8)*(10^(n^2) + 2*10^((n^2 + 3)/4) + 10^((n^2 + 1)/2) + 4*10^((n^2 + n)/2)) if n is odd.

%t Table[1/8*(10^(n^2) + 2*10^((n^2 + 3 #)/4) + (3 - 2 #)*10^((n^2 + #)/2) + (2 + 2 #)*10^((n^2 + n)/2)) &@ Boole@ OddQ@ n, {n, 7}] (* _Michael De Vlieger_, May 12 2017 *)

%Y Column k=10 of A343097.

%Y Cf. A054247, A054739, A054751, A054752, A286392, A286393, A286394, A286395.

%K nonn

%O 0,2

%A _María Merino_, Imanol Unanue, _Yosu Yurramendi_, May 08 2017