cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A367530 The number of ways of tiling the n X n torus up to matrix transposition by a tile that is asymmetric with respect to matrix transposition.

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%I A367530 #28 Jul 08 2024 10:38:10
%S A367530 1,4,32,2081,671104,954448620,5744387279872,144115188176529540,
%T A367530 14925010118699132241920,6338253001141163895983922592,
%U A367530 10985355337065420437221545952731136,77433143050453552574825990883161180320096,2213872302702432822841084717014014514981767643136
%N A367530 The number of ways of tiling the n X n torus up to matrix transposition by a tile that is asymmetric with respect to matrix transposition.
%C A367530 The n X n torus is an n X n grid where two grids are considered the same if one can reach the other by cyclic shifting of rows and columns.
%H A367530 Peter Kagey, <a href="/A367530/a367530_2.pdf">Illustration of a(3) = 32</a>
%H A367530 Peter Kagey and William Keehn, <a href="https://arxiv.org/abs/2311.13072">Counting tilings of the n X m grid, cylinder, and torus</a>, arXiv: 2311.13072 [math.CO], 2023. See also <a href="https://cs.uwaterloo.ca/journals/JIS/VOL27/Kagey/kagey6.html">J. Int. Seq.</a>, (2024) Vol. 27, Art. No. 24.6.1, pp. A-21, A-25.
%t A367530 A367530[n_] := 1/(2n^2) (DivisorSum[n, Function[d, DivisorSum[n, Function[c, EulerPhi[c] EulerPhi[d] 2^(n^2/LCM[c, d])]]]] + n*DivisorSum[n, Function[d, EulerPhi[d]*Which[OddQ[d], 0, EvenQ[d], 2^(n^2/(2 d))]]])
%Y A367530 Cf. A103488, A255015.
%K A367530 nonn
%O A367530 1,2
%A A367530 _Peter Kagey_, Dec 13 2023