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A324144 Triangle read by rows: T(n,k) (1<=k<=n) = number of infinite exponential sequences related to pairs of complementary Fibonacci sequences. 0

%I #6 Feb 20 2019 18:29:42

%S 1,2,1,0,2,0,2,1,1,1,1,2,3,2,3,4,2,0,4,3,0,1,2,3,1,4,3,3,4,1,3,2,2,3,

%T 6,3,4,4,0,2,2,0,3,3,0,1,4,3,2,4,3,4,6,3,3,2,1,3,1,3,3,4,6,3,6,3,2,4,

%U 0,4,4,0,4,3,0,3,3,0,2,1,3,4,4,3,3,4,3,6,6,3,3

%N Triangle read by rows: T(n,k) (1<=k<=n) = number of infinite exponential sequences related to pairs of complementary Fibonacci sequences.

%C The precise definition of this triangle (V(a_1,a_2)) follows the proof of Theorem 5 on page 260.

%H J-P. Bode, H. Harborth, C. Kimberling, <a href="https://www.fq.math.ca/Papers1/45-3/bode.pdf">Complementary Fibonacci sequences</a>, Fibonacci Quarterly 45 (2007), 254-264. See Table 18.

%e Triangle begins:

%e 1,

%e 2,1,

%e 0,2,0,

%e 2,1,1,1,

%e 1,2,3,2,3,

%e 4,2,0,4,3,0,

%e 1,2,3,1,4,3,3,

%e 4,1,3,2,2,3,6,3,

%e 4,4,0,2,2,0,3,3,0,

%e 1,4,3,2,4,3,4,6,3,3,

%e 2,1,3,1,3,3,4,6,3,6,3,

%e 2,4,0,4,4,0,4,3,0,3,3,0,

%e 2,1,3,4,4,3,3,4,3,6,6,3,3,

%e ...

%Y Cf. A022424.

%K nonn,tabl

%O 1,2

%A _N. J. A. Sloane_, Feb 20 2019

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Last modified July 27 18:35 EDT 2024. Contains 374650 sequences. (Running on oeis4.)