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.
%I A366828 #12 Dec 31 2023 00:56:46 %S A366828 0,4,0,88,24,4,0,136,0,220,0,88,48,52,24,136 %N A366828 Number of linearly independent solutions to the neighbor sum problem on a 4-dimensional chessboard of length (3n-1). %C A366828 We say that a chessboard filled with integer entries satisfies the neighbor-sum property if the number appearing on each cell is the sum of entries in its neighboring cells, where neighbors are cells sharing a common edge or vertex. It has been proven in the paper by Dutta et al. that an n X n chessboard satisfies this property if and only if 6 divides (n+1). The sequence at hand deals with the analogous problem in 4 dimensions. %C A366828 It has been proved that if the number of linearly independent solutions to the neighbor sum problem on a 4-dimensional chessboard of length n is nonzero, then 3 divides (n+1) -- see Theorem 28 of Dutta et al. So, the sequence at hand considers a(n) = b(3*n-1) where b(n) is the number of linearly independent solutions to the neighbor sum problem on a 4-dimensional chessboard of length n. %H A366828 Sayan Dutta, Ayanava Mandal, Sohom Gupta, and Sourin Chatterjee, <a href="https://arxiv.org/abs/2310.04401">Neighbour Sum Patterns: Chessboards to Toroidal Worlds</a>, arXiv:2310.04401 [math.NT], 2023. %e A366828 The case of n=2 corresponds to a 5 X 5 X 5 X 5 chessboard. Examples for the analogous problem in two dimensions are given in the paper by Dutta et al. Examples for the analogous problem in three dimensions are given in A366410. %Y A366828 Cf. A366410. %K A366828 nonn,more %O A366828 1,2 %A A366828 _Sayan Dutta_, Oct 25 2023