A348643 a(n) = (16*n + 1)*(2592*n^2 + 288*n + 7).

7, 49079, 361383, 1185751, 2771015, 5366007, 9219559, 14580503, 21697671, 30819895, 42196007, 56074839, 72705223, 92335991, 115215975, 141594007, 171718919, 205839543, 244204711, 287063255, 334664007, 387255799, 445087463, 508407831, 577465735, 652510007, 733789479, 821552983

Offset

0,1

Comments

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.

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

Paolo Xausa, Table of n, a(n) for n = 0..10000

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).

Example

From Elmo R. Oliveira, Sep 03 2025: (Start)
G.f.: (7 + 49051*x + 165109*x^2 + 34665*x^3)/(x-1)^4.
E.g.f.: (7 + 49072*x + 131616*x^2 + 41472*x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). (End)

Mathematica

A348643[n_] := (16*n + 1)*(288*n*(9*n + 1) + 7);
Array[A348643, 30, 0] (* Paolo Xausa, Jun 30 2026 *)

Prog

(PARI) a(n) = (16*n + 1)*(2592*n^2 + 288*n + 7);

Crossrefs

Cf. A000004, A007395, A010701, A348644, A348645, A348646.

Sequence in context: A033984 A309411 A368065 * A123062 A300201 A194194

Adjacent sequences: A348640 A348641 A348642 * A348644 A348645 A348646

Keyword

nonn,easy,changed

Author

Michel Marcus, Oct 27 2021

Status

approved