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A175739 Triangle T(n,m) with the coefficient [x^m] of the polynomial x^(2*n) - x^(2*n - 1) - x^n - x + 1 in row n, column m, 1 <= m <= 2*n. T(0,0) = 1.

%I A175739 #15 Nov 03 2018 19:05:08
%S A175739 1,1,-3,1,1,-1,-1,-1,1,1,-1,0,-1,0,-1,1,1,-1,0,0,-1,0,0,-1,1,1,-1,0,0,
%T A175739 0,-1,0,0,0,-1,1,1,-1,0,0,0,0,-1,0,0,0,0,-1,1,1,-1,0,0,0,0,0,-1,0,0,0,
%U A175739 0,0,-1,1,1,-1,0,0,0,0,0,0,-1,0,0,0,0,0,0,-1,1,1,-1,0,0,0,0,0,0,0
%N A175739 Triangle T(n,m) with the coefficient [x^m] of the polynomial x^(2*n) - x^(2*n - 1) - x^n - x + 1 in row n, column m, 1 <= m <= 2*n. T(0,0) = 1.
%C A175739 The polynomials up to n = 10 are Salem polynomials (the third lowest Salem in the table).
%H A175739 Michael Mossinghoff, <a href="http://www.cecm.sfu.ca/~mjm/Lehmer/lists/SalemList.html">Small Salem Numbers</a>
%H A175739 William J. Floyd, <a href="http://dx.doi.org/10.1007/BF01444729">Growth of planar Coxeter groups, P.V. numbers, and Salem numbers</a>, Math. Ann. Vol. 293 (1992), 475-483.
%F A175739 Sum_{m=0..2*n} T(n,m)= -1.
%F A175739 From _Franck Maminirina Ramaharo_, Nov 02 2018: (Start)
%F A175739 G.f.: (1 - 4*x*y + x*(2 + x + 2*x^2)*y^2 - x^2*(1 + x^2)*y^3)/((1 - y)*(1 - x*y)*(1 - x^2*y)).
%F A175739 E.g.f.: (-(1 - x)*exp(x^2*y) - x*exp(x*y) + x*(1 - x)*exp(y) + 1 + x^2)/x. (End)
%e A175739 The polynomial coefficients are
%e A175739   1;
%e A175739   1, -3,  1;
%e A175739   1, -1, -1, -1,  1;
%e A175739   1, -1,  0, -1,  0, -1,  1;
%e A175739   1, -1,  0,  0, -1,  0,  0, -1,  1;
%e A175739   1, -1,  0,  0,  0, -1,  0,  0,  0, -1,  1;
%e A175739   1, -1,  0,  0,  0,  0, -1,  0,  0,  0,  0, -1, 1;
%e A175739   1, -1,  0,  0,  0,  0,  0, -1,  0,  0,  0,  0, 0, -1, 1;
%e A175739   1, -1,  0,  0,  0,  0,  0,  0, -1,  0,  0,  0, 0,  0, 0, -1, 1;
%e A175739   1, -1,  0,  0,  0,  0,  0,  0,  0, -1,  0,  0, 0,  0, 0,  0, 0, -1, 1;
%e A175739   1, -1,  0,  0,  0,  0,  0,  0,  0,  0, -1,  0, 0,  0, 0,  0, 0,  0, 0, -1, 1;
%e A175739   ...
%e A175739 The corresponding Mahler measures are
%e A175739   -----------------------------------------------------
%e A175739   n | M(p_n)                ||  n | M(p_n)
%e A175739   -----------------------------------------------------
%e A175739   1 | 1.7220838057390422450 ||  6 | 1.2612309611
%e A175739   2 | 1.5061356795538388    ||  7 | 1.2363179318
%e A175739   3 | 1.40126836793         ||  8 | 1.21639166113826509
%e A175739   4 | 1.337313210201        ||  9 | 1.200026523
%e A175739   5 | 1.293485953125        || 10 | 1.286735
%e A175739   ...
%t A175739 p[x_, n_] = If[n == 0, 1, x^(2*n) - x^(2*n - 1) - x^n - x + 1];
%t A175739 Table[CoefficientList[p[x, n], x], {n, 0, 10}]//Flatten
%o A175739 (Maxima) T(n, k) := if n = 0 and k = 0 then 1 else ratcoef(x^(2*n) - x^(2*n - 1) - x^n - x + 1, x, k)$
%o A175739 create_list(T(n, k), n, 0, 10, k, 0, 2*n); /* _Franck Maminirina Ramaharo_, Nov 02 2018 */
%Y A175739 Cf. A143439.
%K A175739 sign,easy,tabf
%O A175739 0,3
%A A175739 _Roger L. Bagula_, Dec 04 2010