The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A068253 1/3 of the number of colorings of an n X n square array with 3 colors. 4
 1, 6, 82, 2604, 193662, 33865632, 13956665236, 13574876544396, 31191658416342674, 169426507164530254380, 2176592549084872196370724, 66158464020552857153017287240, 4759146677426447759184119036493676, 810410082813497381147177065840601910384 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..24 FORMULA For formula see A078099. MATHEMATICA 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 *) CROSSREFS Cf. A068239-A068305, A000332, A002417, A027441, A182368, A182406. See A047938 for number of improper colorings. Main diagonal of A078099. Twice A207993 for n>1. Sequence in context: A089397 A089701 A251584 * A188806 A155811 A239170 Adjacent sequences:  A068250 A068251 A068252 * A068254 A068255 A068256 KEYWORD nonn AUTHOR R. H. Hardin, Feb 24 2002 EXTENSIONS More terms from Vladeta Jovovic, Jul 22 2004 a(11)-a(12) from Alois P. Heinz, Mar 25 2009 a(13)-a(14) from Andrew Howroyd, Jun 26 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified January 19 19:30 EST 2021. Contains 340270 sequences. (Running on oeis4.)