A210574 Lower triangular matrix in the LU-decomposition of the Vandermonde determinants generated by Fibonacci numbers.

1, 1, 1, 1, 3, 1, 1, 7, 12, 1, 1, 15, 50, 264, 1, 1, 31, 180, 1920, 11970, 1, 1, 63, 602, 11760, 146160, 1689600, 1, 1, 127, 1932, 66024, 1477980, 34214400, 603233280, 1, 1, 255, 6050, 353304, 13556970, 568656000, 20043279360, 586244602944, 1

Offset

0,5

Comments

If the Vandermonde matrix V = [F(i+2)^j]_(i,j=0)^n has LU-decomposition, then this triangle is given by L.

Links

Vincenzo Librandi, Rows n = 0..70, flattened

Example

The triangle begins:
1
1, 1
1, 3,   1
1, 7,   12,   1
1, 15,  50,   264,    1
1, 31,  180,  1920,   11970,    1
1, 63,  602,  11760,  146160,   1689600,   1
1, 127, 1932, 66024,  1477980,  34214400,  603233280,   1
1, 255, 6050, 353304, 13556970, 568656000, 20043279360, 586244602944, 1

Mathematica

n = 10; f = Fibonacci[Range[2, n + 1]]; m = Outer[ Power, f, Range[0, n - 1]]; mi = Transpose[LUDecomposition[m][[1]]]; Flatten[Table[Append[Take[mi[[i]], i - 1], 1], {i, n}]] (* T. D. Noe, Mar 22 2012 *)

Crossrefs

Cf. A203311, A210341.

Sequence in context: A075440 A137470 A112492 * A353532 A049290 A297191

Adjacent sequences: A210571 A210572 A210573 * A210575 A210576 A210577

Keyword

nonn,tabl

Author

Emanuele Munarini, Mar 22 2012

Status

approved