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 A368138 The number of ways of tiling the n X n torus up to the symmetries of the square by an asymmetric tile. 4
 1, 154, 1864192, 2199026796168, 188894659314785812480, 1126800533536206914843196839296, 455117248949604553908892209645884928950272, 12259964326927110866866776228808161337250421224373748224, 21812926725659065797324660502998994022561529591086874194578215566049280 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..9. Dan Davis, On a Tiling Scheme from M. C. Escher, Electron. J. Combin. 4(2) (1996), #R23. Peter Kagey, Illustration of a(2)=154 Peter Kagey and William Keehn, Counting tilings of the n X m grid, cylinder, and torus, arXiv: 2311.13072 [math.CO], 2023. MATHEMATICA A368138[n_] := 1/(8n^2)*(DivisorSum[n, Function[d, DivisorSum[n, Function[c, EulerPhi[c] EulerPhi[d] 8^(n^2/LCM[c, d])]]]] + If[EvenQ[n], n^2 (3/4*8^(n^2/2) + 8^(n^2/4)) + n*DivisorSum[n, Function[c, EulerPhi[c] (If[EvenQ[c], 2*8^(n^2/c), 8^(n^2/(2 c))])]], 0] + 2*n*DivisorSum[n, Function[d, EulerPhi[d]*If[EvenQ[d], 8^(n^2/(2 d)), 0]]]) CROSSREFS Cf. A255016, A295223, A367525, A367533, A367534, A367535, A367536, A368137. Sequence in context: A227977 A282557 A200709 * A248657 A159258 A214472 Adjacent sequences: A368135 A368136 A368137 * A368139 A368140 A368141 KEYWORD nonn AUTHOR Peter Kagey, Dec 16 2023 STATUS approved

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Last modified June 25 18:50 EDT 2024. Contains 373707 sequences. (Running on oeis4.)