A071784 Determinant of the n X n matrix whose element (i,j) equals the floor( Phi^(i-j) + 1).

2, 2, 1, -1, -2, -3, -2, -2, 0, -1, 1, -2, 1, -4, 2, -6, 5, -9, 10, -15, 18, -26, 32, -45, 57, -78, 101, -136, 178, -238, 313, -417, 550, -731, 966, -1282, 1696, -2249, 2977, -3946, 5225, -6924, 9170, -12150, 16093, -21321, 28242, -37415, 49562, -65658, 86976

Offset

1,1

Comments

If instead the element (i,j) equals the floor( Phi^(i-j)), the sequence is a series of 1's (A000012).

If instead the element (i,j) equals the ceiling( Phi^(i-j)), the sequence is a series of 1's and -1's (A033999).

If instead the element (i,j) equals the ceiling( Phi^(i-j)+1), the sequence is a series of 2's and -2's: 2*(A033999)=-(-1)^n*(A007395).

Links

Table of n, a(n) for n=1..51.

Formula

G.f.: (-3x^2+2)/[(1-x)(1-x^2+x^3)].

Mathematica

f[n_] := Det[ Table[ Floor[ GoldenRatio^(i - j) + 1], {i, 1, n}, {j, 1, n}]]; Table[ f[n], {n, 1, 55}]

Crossrefs

Cf. A001622.

Sequence in context: A237265 A035463 A245424 * A161638 A066030 A025863

Adjacent sequences: A071781 A071782 A071783 * A071785 A071786 A071787

Keyword

sign

Author

Robert G. Wilson v, Jun 05 2002

Status

approved