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Absolute value of product of nonzero eigenvalues of upper left (n+1)X(n+1) rank 2 submatrix of Wythoff array.
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%I #8 Mar 04 2018 23:33:47

%S 1,1,4,8,20,38,77,143,267,474,856,1540,2703,4749,8204,14233,24714,

%T 42234,72495,122930,209534,357733,603816,1023096,1735667,2915260,

%U 4913350,8216036,13794118,23198608,38710749,64802028,108623872,180780234,301734372,500717764,833682438,1390233453,2304627170

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

%C Empirical observation via computation.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Wythoff_array">Wythoff array</a>

%e a(1) = 1 = |(4 + sqrt(17))*(4 - sqrt(17))|;

%e a(2) = 1 = |(12 + sqrt(145))*(1/(-12 - sqrt(145)))|;

%e a(3) = 4 = (1/2)*(63 + sqrt(3985))*(8/(-63 - sqrt(3985))).

%t \[Phi] = (1 + Sqrt[5])/2;

%t A[m_, 1] := Floor[Floor[m*\[Phi]]*\[Phi]]

%t A[m_, 2] := Floor[Floor[m*\[Phi]]*\[Phi]^2]

%t A[m_, n_] := A[m, n] = A[m, n - 1] + A[m, n - 2]

%t M[n_] := Table[A[i, j], {i, 1, n}, {j, 1, n}]

%t X = Table[{n, -Simplify[Eigenvalues[M[n]][[1 ;; 2]][[1]]*Eigenvalues[M[n]][[1 ;; 2]][[2]]]}, {n, 2, 40}]

%Y Cf. A035513.

%K nonn

%O 1,3

%A _Gary E. Davis_, Feb 26 2018