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 A348644 #12 Sep 04 2025 08:41:06 %S A348644 11,73625,542087,1778645,4156547,8049041,13829375,21870797,32546555, %T A348644 46229897,63294071,84112325,109057907,138504065,172824047,212391101, %U A348644 257578475,308759417,366307175,430594997,501996131,580883825,667631327,762611885,866198747,978765161,1100684375 %N A348644 a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11). %C A348644 a(n) is the entry (1,2) 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 A348644 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 A348644 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 A348644 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodular_matrix">Unimodular matrix</a>. %H A348644 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A348644 From _Elmo R. Oliveira_, Sep 03 2025: (Start) %F A348644 G.f.: (11 + 73581*x + 247653*x^2 + 52003*x^3)/(x-1)^4. %F A348644 E.g.f.: (11 + 73614*x + 197424*x^2 + 62208*x^3)*exp(x). %F A348644 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) %o A348644 (PARI) a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11); %Y A348644 Cf. A000004, A007395, A010701, A348643, A348645, A348646. %K A348644 nonn,easy,changed %O A348644 0,1 %A A348644 _Michel Marcus_, Oct 27 2021