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 A348643 #13 Sep 04 2025 08:41:13 %S A348643 7,49079,361383,1185751,2771015,5366007,9219559,14580503,21697671, %T A348643 30819895,42196007,56074839,72705223,92335991,115215975,141594007, %U A348643 171718919,205839543,244204711,287063255,334664007,387255799,445087463,508407831,577465735,652510007,733789479,821552983 %N A348643 a(n) = (16*n + 1)*(2592*n^2 + 288*n + 7). %C A348643 a(n) is the entry (1,1) 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 A348643 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 A348643 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 A348643 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodular_matrix">Unimodular matrix</a>. %H A348643 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1). %e A348643 From _Elmo R. Oliveira_, Sep 03 2025: (Start) %e A348643 G.f.: (7 + 49051*x + 165109*x^2 + 34665*x^3)/(x-1)^4. %e A348643 E.g.f.: (7 + 49072*x + 131616*x^2 + 41472*x^3)*exp(x). %e A348643 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End) %o A348643 (PARI) a(n) = (16*n + 1)*(2592*n^2 + 288*n + 7); %Y A348643 Cf. A000004, A007395, A010701, A348644, A348645, A348646. %K A348643 nonn,easy,changed %O A348643 0,1 %A A348643 _Michel Marcus_, Oct 27 2021