A394646 - OEIS

%I #34 May 15 2026 05:39:36

%S 11,-11101,1102,111111101,-11122203,11103,-11112121211101,

%T 1113242533304,-1121433306,111104,11112222323222211101,

%U -1113344758667744405,1122547669966610,-112225544410,1111105,-111122324344444434232211101,11133549812244525939955506,-11226591166972437711015,1123378103995511020,-11223276655515,11111106

%N 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.

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

%H Amiram Eldar, <a href="/A394646/b394646.txt">Table of n, a(n) for n = 1..465</a> (first 30 rows, flattened)

%H Ahmad J. Masad, <a href="https://mathoverflow.net/q/281442">Conjecture that relates matrix systems with some polynomials of integer coefficients as solution sets</a>, MathOverflow, Sep 2017.

%e Triangle begins:

%e                     11;

%e                 -11101,                 1102;

%e              111111101,            -11122203,            11103;

%e        -11112121211101,        1113242533304,      -1121433306,        111104;

%e   11112222323222211101, -1113344758667744405, 1122547669966610, -112225544410, 1111105;

%e   ...

%o (PARI) M(n) = matrix(n, n, i, j, ((10^(i+1) + 1)^(j-1) + 9)/10);

%o b(n) = vector(n, i, ((10^(i+1)+1)^n + 9)/10);

%o row(n) = matsolve(M(n), b(n)~)~;

%Y Cf. A365450, A292625.

%K sign,tabl

%O 1,1

%A _Ahmad J. Masad_, Apr 28 2026