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

1, 1, 4, 8, 20, 38, 77, 143, 267, 474, 856, 1540, 2703, 4749, 8204, 14233, 24714, 42234, 72495, 122930, 209534, 357733, 603816, 1023096, 1735667, 2915260, 4913350, 8216036, 13794118, 23198608, 38710749, 64802028, 108623872, 180780234, 301734372, 500717764, 833682438, 1390233453, 2304627170

Offset: 1

Author

Gary E. Davis, Feb 26 2018

Keywords

• nonn

Comments

Empirical observation via computation.

Examples

			a(1) = 1 = |(4 + sqrt(17))*(4 - sqrt(17))|;
a(2) = 1 = |(12 + sqrt(145))*(1/(-12 - sqrt(145)))|;
a(3) = 4 = (1/2)*(63 + sqrt(3985))*(8/(-63 - sqrt(3985))).
		

Links

• Wikipedia, Wythoff array

Crossrefs

Cf. A035513.

Programs

Mathematica

\[Phi] = (1 + Sqrt[5])/2;
A[m_, 1] := Floor[Floor[m*\[Phi]]*\[Phi]]
A[m_, 2] := Floor[Floor[m*\[Phi]]*\[Phi]^2]
A[m_, n_] := A[m, n] = A[m, n - 1] + A[m, n - 2]
M[n_] := Table[A[i, j], {i, 1, n}, {j, 1, n}]
X = Table[{n, -Simplify[Eigenvalues[M[n]][[1 ;; 2]][[1]]*Eigenvalues[M[n]][[1 ;; 2]][[2]]]}, {n, 2, 40}]