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%I #20 Nov 01 2017 12:20:09
%S 1,6,82,2604,193662,33865632,13956665236,13574876544396,
%T 31191658416342674,169426507164530254380,2176592549084872196370724,
%U 66158464020552857153017287240,4759146677426447759184119036493676,810410082813497381147177065840601910384
%N 1/3 of the number of colorings of an n X n square array with 3 colors.
%H Andrew Howroyd, <a href="/A068253/b068253.txt">Table of n, a(n) for n = 1..24</a>
%F For formula see A078099.
%t M[1] = {{1}}; M[m_] := M[m] = {{M[m - 1], Transpose[M[m - 1]]}, {Array[0 &, {2^(m - 2), 2^(m - 2)}], M[m - 1]}} // ArrayFlatten; W[m_] := M[m] + Transpose[M[m]]; T[m_, 1] := 2^(m - 1); T[1, n_] := 2^(n - 1); T[m_, n_] := MatrixPower[W[m], n - 1] // Flatten // Total; a[n_] := T[n, n]; Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 12}] (* _Jean-François Alcover_, Nov 01 2017, after code from A078099 *)
%Y Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406.
%Y See A047938 for number of improper colorings.
%Y Main diagonal of A078099.
%Y Twice A207993 for n>1.
%K nonn
%O 1,2
%A _R. H. Hardin_, Feb 24 2002
%E More terms from _Vladeta Jovovic_, Jul 22 2004
%E a(11)-a(12) from _Alois P. Heinz_, Mar 25 2009
%E a(13)-a(14) from _Andrew Howroyd_, Jun 26 2017
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