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 A348645 #12 Sep 04 2025 10:53:24 %S A348645 13,74581,545725,1786693,4170733,8071093,13861021,21913765,32602573, %T A348645 46300693,63381373,84217861,109183405,138651253,172994653,212586853, %U A348645 257801101,309010645,366588733,430908613,502343533,581266741,668051485,763071013,866698573,979307413,1101270781 %N A348645 a(n) = (12*n + 1)*(5184*n^2 + 540*n + 13). %C A348645 a(n) is the entry (2,1) of a family of unimodular matrices none of whose entries is 1 or -1, such that when each entry of the matrix is replaced by its cube, the resulting matrix is also unimodular. %C A348645 In these matrices, the entries (1,3) and (3,1) = 2; the entries (2,3) and (3,2) = 3; the entry (3,3) = 0. %H A348645 Ajai Choudhry, <a href="https://arxiv.org/abs/2110.12643">A diophantine problem concerning third order matrices</a>, arXiv:2110.12643 [math.NT], 2021. %H A348645 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodular_matrix">Unimodular matrix</a>. %H A348645 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A348645 From _Elmo R. Oliveira_, Sep 04 2025: (Start) %F A348645 G.f.: (13 + 74529*x + 247479*x^2 + 51227*x^3)/(x-1)^4. %F A348645 E.g.f.: (13 + 74568*x + 198288*x^2 + 62208*x^3)*exp(x). %F A348645 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) %o A348645 (PARI) a(n) = (12*n + 1)*(5184*n^2 + 540*n + 13); %Y A348645 Cf. A000004, A007395, A010701, A348643, A348644, A348646. %K A348645 nonn,easy,changed %O A348645 0,1 %A A348645 _Michel Marcus_, Oct 27 2021