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 A376132 #23 Aug 22 2025 13:26:29 %S A376132 1,1,4,1,4,1,11,1,4,1,11,1,4,1,26,1,4,1,11,1,4,1,26,1,4,1,11,1,4,1,57, %T A376132 1,4,1,11,1,4,1,26,1,4,1,11,1,4,1,57,1,4,1,11,1,4,1,26,1,4,1,11,1,4,1, %U A376132 120,1,4,1,11,1,4,1,26,1,4,1,11,1,4,1,57,1,4,1,11,1,4,1,26,1 %N A376132 First differences of A376131. %C A376132 The sequence consists of Eulerian numbers from A000295. %C A376132 The total number of fires for 2n and 2n-1 chips is the same, this is why the interesting increase is 2. %H A376132 Dillan Agrawal, Selena Ge, Jate Greene, Tanya Khovanova, Dohun Kim, Rajarshi Mandal, Tanish Parida, Anirudh Pulugurtha, Gordon Redwine, Soham Samanta, and Albert Xu, <a href="https://arxiv.org/abs/2501.06675">Chip-Firing on Infinite k-ary Trees</a>, arXiv:2501.06675 [math.CO], 2025. See p. 17. %H A376132 Ryota Inagaki, Tanya Khovanova, and Austin Luo, <a href="https://doi.org/10.1007/s00026-025-00779-6">On Chip-Firing on Undirected Binary Trees</a>, Ann. Comb. (2025). See p. 24. %H A376132 Wikipedia, <a href="https://en.wikipedia.org/wiki/Chip-firing_game">Chip-firing game</a>. %F A376132 a(n) = A000295(A376116(n+1) - A376116(n) + 1). %p A376132 b:= n-> (l-> add(((i-2)*2^(i-1)+1)*(l[i]+1), i=2..nops(l)-1))(Bits[Split](2*n+1)): %p A376132 a:= n-> b(n+1)-b(n): %p A376132 seq(a(n), n=1..88); # _Alois P. Heinz_, Sep 12 2024 %Y A376132 Cf. A000295, A091090, A376116, A376131. %K A376132 nonn %O A376132 1,3 %A A376132 _Ryota Inagaki_, _Tanya Khovanova_, and _Austin Luo_, Sep 11 2024