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%I #27 Dec 11 2019 07:11:54
%S 1,1,1,2,1,3,1,5,5,1,6,8,1,8,19,13,1,9,25,21,1,11,42,65,34,1,12,51,90,
%T 55,1,14,74,183,210,89,1,15,86,234,300,144,1,17,115,394,717,654,233,6,
%U 18,130,480,951,954,377,1,20,165,725,1825,2622,1985,610,1,21,183,855
%N Triangle read by rows, Fibonacci product polynomials.
%C The polynomials demonstrate the Fibonacci product formula: F(n) = Product_{k=1..(n-1)/2} (1 + 4*cos^2(k*Pi)/n).
%C Row sums give A002530.
%C The triangle A125076 is formed by reading upward sloping diagonals. - _Gary W. Adamson_, Nov 26 2008
%C Bisection of the triangle: odd-indexed rows are reversals of the rows of A126124, even-indexed rows are the reversals of the rows of A123965. - Gary W. Adamson_, Aug 15 2010
%H James P. Bradshaw, Philipp Lampe, Dusan Ziga, <a href="https://arxiv.org/abs/1910.11823">Snake graphs and their characteristic polynomials</a>, arXiv:1910.11823 [math.CO], 2019. See 4.7 p. 16.
%H N. D. Cahill and D. A. Narayan, <a href="http://www.fq.math.ca/Papers1/42-3/quartcahill03_2004.pdf">Fibonacci and Lucas Numbers as Tridiagonal Matrix Determinants</a>, Fibonacci Quarterly, 42(3):216-221, 2004.
%H M. X. He, D. Simon and P. E. Ricci, <a href="http://www.fq.math.ca/Scanned/35-2/he.pdf">Dynamics of the zeros of Fibonacci polynomials</a>, Fibonacci Quarterly, 35(2):160-168, 1997.
%H V. E. Hoggatt and C. T. Long, <a href="http://www.fq.math.ca/Scanned/12-2/hoggatt1.pdf">Divisibility Properties of Generalized Fibonacci Polynomials</a>, Fibonacci Quarterly, 12:113-120, 1974.
%e First few rows of the triangle are:
%e 1;
%e 1;
%e 1, 2;
%e 1, 3;
%e 1, 5, 5;
%e 1, 6, 8;
%e 1, 8, 19, 13;
%e 1, 9, 25, 21;
%e 1, 11, 42, 65, 34;
%e 1, 12, 51, 90, 55;
%e 1, 14, 74, 183, 210, 89;
%e 1, 15, 86, 234, 300, 144;
%e 1, 17, 115, 394, 717, 654, 233;
%e 1, 18, 130, 480, 951, 954, 377;
%e 1, 20, 165, 725, 1825, 2622, 1985, 610;
%e 1, 21, 183, 855, 2305, 3573, 2939, 987;
%e 1, 23, 224, 1203, 3885, 7703, 9134, 5911, 1597;
%e 1, 24, 245, 1386, 4740, 10008, 12707, 8850, 2584;
%e 1, 26, 292, 1855, 7329, 18633, 30418, 30691, 17345, 4181;
%e 1, 27, 316, 2100, 8715, 23373, 40426, 43398, 26195, 6765;
%e 1, 29, 369, 2708, 12670, 39417, 82432, 114242, 100284, 50305, 10946;
%e 1, 30, 396, 3024, 14770, 48132, 105805, 154668, 143682, 76500, 17711;
%e ...
%e By row, alternate signs (+,-,+,-,...) with descending exponents. Rows with n terms have exponents (n-1), (n-2), (n-3),...;
%e Example: There are two rows with 4 terms corresponding to the polynomials
%e x^3 - 8x^2 + 19x - 13 (roots associated with the heptagon); and
%e x^3 - 9x^2 + 25x - 21 (roots associated with the 9-gon (nonagon)).
%Y Cf. A000045, A002530.
%Y Cf. A125076. - _Gary W. Adamson_, Nov 26 2008
%Y Cf. A126124, A123965. - _Gary W. Adamson_, Aug 15 2010
%K nonn,tabf
%O 1,4
%A _Gary W. Adamson_ & _Roger L. Bagula_, Nov 22 2008
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