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

1,3

Comments

Empirical observation via computation.

Links

Table of n, a(n) for n=1..39.

Wikipedia, Wythoff array

Example

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))).

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}]

Crossrefs

Cf. A035513.

Sequence in context: A280486 A097940 A032280 * A156303 A301138 A008136

Adjacent sequences: A300155 A300156 A300157 * A300159 A300160 A300161

Keyword

nonn

Author

Gary E. Davis, Feb 26 2018

Status

approved