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 A348646 #12 Sep 04 2025 10:53:19 %S A348646 20,111881,818606,2680067,6256136,12106685,20791586,32870711,48903932, %T A348646 69451121,95072150,126326891,163775216,207976997,259492106,318880415, %U A348646 386701796,463516121,549883262,646363091,753515480,871900301,1002077426,1144606727,1300048076,1468961345,1651906406 %N A348646 a(n) = (72*n + 5)*(1296*n^2 + 153*n + 4). %C A348646 a(n) is the entry (2,2) 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 A348646 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 A348646 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 A348646 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodular_matrix">Unimodular matrix</a>. %H A348646 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %F A348646 From _Elmo R. Oliveira_, Sep 04 2025: (Start) %F A348646 G.f.: (20 + 111801*x + 371202*x^2 + 76849*x^3)/(x-1)^4. %F A348646 E.g.f.: (20 + 111861*x + 297432*x^2 + 93312*x^3)*exp(x). %F A348646 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) %o A348646 (PARI) a(n) = (72*n + 5)*(1296*n^2 + 153*n + 4); %Y A348646 Cf. A000004, A007395, A010701, A348643, A348644, A348645. %K A348646 nonn,easy,changed %O A348646 0,1 %A A348646 _Michel Marcus_, Oct 27 2021