A394646 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) = ((10^(i+1) + 1)^(j-1) + 9)/10 and b(i) = ((10^(i+1)+1)^n + 9)/10 for 1 <= i,j <= n.

11, -11101, 1102, 111111101, -11122203, 11103, -11112121211101, 1113242533304, -1121433306, 111104, 11112222323222211101, -1113344758667744405, 1122547669966610, -112225544410, 1111105, -111122324344444434232211101, 11133549812244525939955506, -11226591166972437711015, 1123378103995511020, -11223276655515, 11111106

Offset

1,1

Comments

This sequence is similar to A292625 and A365450. See the MathOverflow link.

Links

Amiram Eldar, Table of n, a(n) for n = 1..465 (first 30 rows, flattened)

Ahmad J. Masad, Conjecture that relates matrix systems with some polynomials of integer coefficients as solution sets, MathOverflow, Sep 2017.

Example

Triangle begins:
                    11;
                -11101,                 1102;
             111111101,            -11122203,            11103;
       -11112121211101,        1113242533304,      -1121433306,        111104;
  11112222323222211101, -1113344758667744405, 1122547669966610, -112225544410, 1111105;
  ...

Prog

(PARI) M(n) = matrix(n, n, i, j, ((10^(i+1) + 1)^(j-1) + 9)/10);
b(n) = vector(n, i, ((10^(i+1)+1)^n + 9)/10);
row(n) = matsolve(M(n), b(n)~)~;

Crossrefs

Cf. A365450, A292625.

Sequence in context: A068224 A066945 A267359 * A267940 A384015 A113615

Adjacent sequences: A394643 A394644 A394645 * A394647 A394648 A394649

Keyword

sign,tabl

Author

Ahmad J. Masad, Apr 28 2026

Status

approved