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A210574 Lower triangular matrix in the LU-decomposition of the Vandermonde determinants generated by Fibonacci numbers. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A049290 A297191 A147990

Adjacent sequences:  A210571 A210572 A210573 * A210575 A210576 A210577

KEYWORD

nonn,tabl

AUTHOR

Emanuele Munarini, Mar 22 2012

STATUS

approved

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)