The OEIS is supported by the many generous donors to the OEIS Foundation.



Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A294793 Triangle read by rows, 1 <= k <= n: T(n,k) = non-isomorphic colorings of a toroidal n X k grid using exactly four colors under translational symmetry and swappable colors. 8
0, 0, 1, 0, 13, 874, 1, 235, 51075, 10741819, 2, 3437, 2823766, 2261625725, 1870851589562, 13, 51275, 155495153, 486711524815, 1600136051453135, 5465007068038102643, 50, 742651, 8643289534, 107092397450897, 1405227969932349726, 19188864521773558375127, 269482732023591671431784330, 221, 10741763, 486710971595, 24009547064476683 (list; table; graph; refs; listen; history; text; internal format)



Two colorings are equivalent if there is a permutation of the colors that takes one to the other in addition to translational symmetries on the torus. (Power Group Enumeration.)


F. Harary and E. Palmer, Graphical Enumeration, Academic Press, 1973.


Table of n, a(n) for n=1..32.

Marko Riedel et al., Burnside lemma and translational symmetries of the torus.


T(n,k) = (1/(n*k*Q!))*(Sum_{sigma in S_Q} Sum_{d|n} Sum_{f|k} phi(d) phi(f) [[forall j_l(sigma) > 0 : l|lcm(d,f) ]] P(gcd(d,f)*(n/d)*(k/f), sigma)) where P(F, sigma) = F! [z^F] Product_{l=1..Q} (exp(lz)-1)^j_l(sigma) with Q=4. The notation j_l(sigma) is from the Harary text and gives the number of cycles of length l in the permutation sigma. [[.]] is an Iverson bracket.


Cf. A294684, A294685, A294686, A294687, A294791, A294792, A294794, A295197. T(n,1) is A056297.

Sequence in context: A289225 A331341 A123838 * A013539 A201255 A196695

Adjacent sequences: A294790 A294791 A294792 * A294794 A294795 A294796




Marko Riedel, Nov 08 2017



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

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 21:09 EST 2022. Contains 358484 sequences. (Running on oeis4.)