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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A368145 The number of ways of tiling the n X n torus up to 90-degree rotations of the square by an asymmetric tile. 3
 1, 23, 7296, 67124336, 11258999068672, 32794211700912314368, 1616901275801313012113145856, 1329227995784915876578744357489750016, 18043230090504974298810923860695296894480941056, 4017345110647475688854905231100098373350012499289786810368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS M.C. Escher enumerated a(2) = 23 by hand in May 1942, being perhaps the first person to attempt this sort of counting problem. (See Doris Schattschneider's book in the references for more details.) REFERENCES Doris Schattschneider, Visions of Symmetry, W.H. Freeman, 1990, pages 44-48. LINKS Table of n, a(n) for n=1..10. Peter Kagey, Illustration of a(2)=23 Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv: 2311.13072 [math.CO], 2023. Doris Schattschneider, Escher's combinatorial patterns, Electron. J. Combin. 4(2) (1996), #R17. MATHEMATICA A368145[n_] := 1/(4n^2)*(DivisorSum[n, Function[d, DivisorSum[n, Function[c, EulerPhi[c] EulerPhi[d] 4^(n^2/LCM[c, d])]]]] + n^2*If[OddQ[n], 0, 3/4*2^n^2 + 2^(n^2/2)]) CROSSREFS Cf. A367530, A367532, A368138, A368142, A368143, A368144. Sequence in context: A193430 A233213 A368142 * A090674 A013728 A028693 Adjacent sequences: A368142 A368143 A368144 * A368146 A368147 A368148 KEYWORD nonn AUTHOR Peter Kagey, Dec 16 2023 STATUS approved

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.

Last modified June 25 17:15 EDT 2024. Contains 373706 sequences. (Running on oeis4.)