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a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11).
3

%I #8 Oct 27 2021 15:00:00

%S 11,73625,542087,1778645,4156547,8049041,13829375,21870797,32546555,

%T 46229897,63294071,84112325,109057907,138504065,172824047,212391101,

%U 257578475,308759417,366307175,430594997,501996131,580883825,667631327,762611885,866198747,978765161,1100684375

%N a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11).

%C 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 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 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 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodular_matrix">Unimodular matrix</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).

%o (PARI) a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11);

%Y Cf. A000004, A007395, A010701, A348643, A348645, A348646.

%K nonn,easy

%O 0,1

%A _Michel Marcus_, Oct 27 2021