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A368154 Triangular array T(n,k), read by rows: coefficients of strong divisibility sequence of polynomials p(1,x) = 1, p(2,x) = 1 + 3*x, p(n,x) = u*p(n-1,x) + v*p(n-2,x) for n >= 3, where u = p(2,x), v = 1 - 3*x - x^2.

%I A368154 #10 Jan 22 2024 06:04:05
%S A368154 1,1,3,2,3,8,3,9,7,21,5,15,31,15,55,8,30,53,99,30,144,13,54,124,165,
%T A368154 306,54,377,21,99,241,447,481,927,77,987,34,177,487,909,1509,1341,
%U A368154 2767,33,2584,55,315,941,1995,3135,4905,3605,8163,-355,6765,89,555
%N A368154 Triangular array T(n,k), read by rows: coefficients of strong divisibility sequence of polynomials p(1,x) = 1, p(2,x) = 1 + 3*x, p(n,x) = u*p(n-1,x) + v*p(n-2,x) for n >= 3, where u = p(2,x), v = 1 - 3*x - x^2.
%C A368154 Because (p(n,x)) is a strong divisibility sequence, for each integer k, the sequence (p(n,k)) is a strong divisibility sequence of integers.
%H A368154 Rigoberto Flórez, Robinson Higuita, and Antara Mukherjee, <a href="http://math.colgate.edu/~integers/s14/s14.Abstract.html">Characterization of the strong divisibility property for generalized Fibonacci polynomials</a>, Integers, 18 (2018), 1-28, Paper No. A14.
%F A368154 p(n,x) = u*p(n-1,x) + v*p(n-2,x) for n >= 3, where p(1,x) = 1, p(2,x) = 1 + 3*x, u = p(2,x), and v = 1 - 3*x - x^2.
%F A368154 p(n,x) = k*(b^n - c^n), where k = -1/sqrt(5 - 6*x + 5*x^2), b = (1/2)*(3*x + 1 - 1/k), c = (1/2)*(2*x + 1 + 1/k).
%e A368154 First eight rows:
%e A368154    1
%e A368154    1    3
%e A368154    2    3     8
%e A368154    3    9     7    21
%e A368154    5   15    31    15    55
%e A368154    8   30    53    99    30   144
%e A368154   13   54   124   165   306    54  377
%e A368154   21   99   241   447   481   927   77  987
%K A368154 tabl,sign
%O A368154 1,3
%A A368154 _Clark Kimberling_, Jan 20 2024