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

Author

Emanuele Munarini, Mar 22 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			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
		

Links

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

Crossrefs

Cf. A203311, A210341.

Programs

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 *)