A365450 Triangle read by rows: row n gives y transposed, where y is the solution to the matrix equation M*y=b, where the matrix M and vector b are defined by M(i,j) = ((3^(i+1) + 1)^(j-1) + 2)/3 and b(i) = ((3^(i+1)+1)^n + 2)/3 for 1 <= i,j <= n.

4, -118, 38, 9838, -3396, 120, -2413594, 851584, -32676, 364, 1765112266, -627258560, 24705064, -298396, 1094, -3864390160942, 1376531364480, -54681938592, 677595512, -2692068, 3282, 25363211967758062, -9041746935535360, 360199412405184, -4501063688336, 18342945728, -24228552, 9844

Offset: 1

Author

Ahmad J. Masad, Sep 03 2023

Keywords

• sign
• tabl

Comments

This sequence is similar to A292625, see the MathOverflow link.

The matrix M is given by A374258. - Ahmad J. Masad, Jul 29 2024

Examples

			Triangle begins:
         4;
      -118,     38;
      9838,  -3396,    120;
  -2413594, 851584, -32676, 364;
  ...
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..820 (Rows 1..40)
• Ahmad J. Masad, Conjecture that relates matrix systems with some polynomials of integer coefficients as solution sets, MathOverflow, Sep 2017.

Crossrefs

Cf. A292625, A374258.

Programs

PARI

M(n) = matrix(n, n, i, j, ((3^(i+1) + 1)^(j-1) + 2)/3);
b(n) = vector(n, i, ((3^(i+1)+1)^n + 2)/3);
row(n) = matsolve(M(n), b(n)~)~; \\ Michel Marcus, Sep 03 2023

Extensions

More terms from Michel Marcus, Sep 03 2023