A348644 a(n) = (18*n + 1)*(24*n + 1)*(144*n + 11).

11, 73625, 542087, 1778645, 4156547, 8049041, 13829375, 21870797, 32546555, 46229897, 63294071, 84112325, 109057907, 138504065, 172824047, 212391101, 257578475, 308759417, 366307175, 430594997, 501996131, 580883825, 667631327, 762611885, 866198747, 978765161, 1100684375

Offset

0,1

Comments

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.

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).

Formula

From Elmo R. Oliveira, Sep 03 2025: (Start)

G.f.: (11 + 73581*x + 247653*x^2 + 52003*x^3)/(x-1)^4.

E.g.f.: (11 + 73614*x + 197424*x^2 + 62208*x^3)*exp(x).

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Mathematica

Table[(18n+1)(24n+1)(144n+11), {n, 0, 30}] (* Harvey P. Dale, Nov 29 2025 *)
(* Alternative: *)
LinearRecurrence[{4, -6, 4, -1}, {11, 73625, 542087, 1778645}, 30] (* Harvey P. Dale, Nov 29 2025 *)

Prog

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

Crossrefs

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

Sequence in context: A102367 A055322 A390618 * A165934 A110780 A087395

Adjacent sequences: A348641 A348642 A348643 * A348645 A348646 A348647

Keyword

nonn,easy

Author

Michel Marcus, Oct 27 2021

Status

approved