login
Triangle of coefficients in a Fibonacci-like sequence of polynomials.
2

%I #13 Aug 09 2024 01:23:28

%S 1,1,1,-1,1,-1,-1,1,-1,-2,1,1,-1,-3,2,1,1,-1,-4,3,3,-1,1,-1,-5,4,6,-3,

%T -1,1,-1,-6,5,10,-6,-4,1,1,-1,-7,6,15,-10,-10,4,1,1,-1,-8,7,21,-15,

%U -20,10,5,-1,1,-1,-9,8,28,-21,-35,20,15,-5,-1,1,-1,-10

%N Triangle of coefficients in a Fibonacci-like sequence of polynomials.

%C Essentially the same as A108299. - _Philippe Deléham_, Feb 27 2014

%D A. F. Horadam, R. P. Loh and A. G. Shannon, Divisibility properties of some Fibonacci-type sequences, pp. 55-64 of Combinatorial Mathematics VI (Armidale 1978), Lect. Notes Math. 748, 1979.

%F q_{n+2}(x) = x*q_{n+1}(x)-q_n(x), q_1(x) = q_2(x) = 1.

%e Triangle starts:

%e 1

%e 1

%e 1 -1

%e 1 -1 -1

%e 1 -1 -2 1

%e 1 -1 -3 2 1

%e ...

%Y Cf. A065941, A108299.

%K sign,tabf

%O 1,10

%A _N. J. A. Sloane_.

%E More terms from _Philippe Deléham_, Feb 27 2014