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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.
0
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.
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
KEYWORD
nonn
AUTHOR
Gary E. Davis, Feb 26 2018
STATUS
approved