A348645 a(n) = (12*n + 1)*(5184*n^2 + 540*n + 13).

13, 74581, 545725, 1786693, 4170733, 8071093, 13861021, 21913765, 32602573, 46300693, 63381373, 84217861, 109183405, 138651253, 172994653, 212586853, 257801101, 309010645, 366588733, 430908613, 502343533, 581266741, 668051485, 763071013, 866698573, 979307413, 1101270781

Offset

0,1

Comments

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.

In these matrices, the entries (1,3) and (3,1) = 2; the entries (2,3) and (3,2) = 3; the entry (3,3) = 0.

Links

Table of n, a(n) for n=0..26.

Ajai Choudhry, A diophantine problem concerning third order matrices, arXiv:2110.12643 [math.NT], 2021.

Wikipedia, Unimodular matrix

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Prog

(PARI) a(n) = (12*n + 1)*(5184*n^2 + 540*n + 13);

Crossrefs

Cf. A000004, A007395, A010701, A348643, A348644, A348646.

Sequence in context: A203675 A189251 A188980 * A022547 A273217 A176119

Adjacent sequences: A348642 A348643 A348644 * A348646 A348647 A348648

Keyword

nonn,easy

Author

Michel Marcus, Oct 27 2021

Status

approved