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A300158 Absolute value of product of nonzero eigenvalues of upper left (n+1)X(n+1) rank 2 submatrix of Wythoff array.

%I A300158 #8 Mar 04 2018 23:33:47
%S A300158 1,1,4,8,20,38,77,143,267,474,856,1540,2703,4749,8204,14233,24714,
%T A300158 42234,72495,122930,209534,357733,603816,1023096,1735667,2915260,
%U A300158 4913350,8216036,13794118,23198608,38710749,64802028,108623872,180780234,301734372,500717764,833682438,1390233453,2304627170
%N A300158 Absolute value of product of nonzero eigenvalues of upper left (n+1)X(n+1) rank 2 submatrix of Wythoff array.
%C A300158 Empirical observation via computation.
%H A300158 Wikipedia, <a href="https://en.wikipedia.org/wiki/Wythoff_array">Wythoff array</a>
%e A300158 a(1) = 1 = |(4 + sqrt(17))*(4 - sqrt(17))|;
%e A300158 a(2) = 1 = |(12 + sqrt(145))*(1/(-12 - sqrt(145)))|;
%e A300158 a(3) = 4 = (1/2)*(63 + sqrt(3985))*(8/(-63 - sqrt(3985))).
%t A300158 \[Phi] = (1 + Sqrt[5])/2;
%t A300158 A[m_, 1] := Floor[Floor[m*\[Phi]]*\[Phi]]
%t A300158 A[m_, 2] := Floor[Floor[m*\[Phi]]*\[Phi]^2]
%t A300158 A[m_, n_] := A[m, n] = A[m, n - 1] + A[m, n - 2]
%t A300158 M[n_] := Table[A[i, j], {i, 1, n}, {j, 1, n}]
%t A300158 X = Table[{n, -Simplify[Eigenvalues[M[n]][[1 ;; 2]][[1]]*Eigenvalues[M[n]][[1 ;; 2]][[2]]]}, {n, 2, 40}]
%Y A300158 Cf. A035513.
%K A300158 nonn
%O A300158 1,3
%A A300158 _Gary E. Davis_, Feb 26 2018