cp's OEIS Frontend

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.

%I A365450 #27 Aug 19 2024 11:44:51
%S A365450 4,-118,38,9838,-3396,120,-2413594,851584,-32676,364,1765112266,
%T A365450 -627258560,24705064,-298396,1094,-3864390160942,1376531364480,
%U A365450 -54681938592,677595512,-2692068,3282,25363211967758062,-9041746935535360,360199412405184,-4501063688336,18342945728,-24228552,9844
%N 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.
%C A365450 This sequence is similar to A292625, see the MathOverflow link.
%C A365450 The matrix M is given by A374258. - _Ahmad J. Masad_, Jul 29 2024
%H A365450 Michel Marcus, <a href="/A365450/b365450.txt">Table of n, a(n) for n = 1..820</a> (Rows 1..40)
%H A365450 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 A365450 Triangle begins:
%e A365450          4;
%e A365450       -118,     38;
%e A365450       9838,  -3396,    120;
%e A365450   -2413594, 851584, -32676, 364;
%e A365450   ...
%o A365450 (PARI) M(n) = matrix(n, n, i, j, ((3^(i+1) + 1)^(j-1) + 2)/3);
%o A365450 b(n) = vector(n, i, ((3^(i+1)+1)^n + 2)/3);
%o A365450 row(n) = matsolve(M(n), b(n)~)~; \\ _Michel Marcus_, Sep 03 2023
%Y A365450 Cf. A292625, A374258.
%K A365450 sign,tabl
%O A365450 1,1
%A A365450 _Ahmad J. Masad_, Sep 03 2023
%E A365450 More terms from _Michel Marcus_, Sep 03 2023