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A158472
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Triangle read by rows generated from Fibonaccci numbers as polynomials: (x-F1)*(x-F2)*(x-F3)*...*(x-Fn)
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2
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1, 1, -1, 1, -2, 1, 1, -4, 5, -2, 1, -7, 17, -17, 6, 1, -12, 52, -102, 91, -30, 1, -20, 148, -518, 907, -758, 240, 1, -33, 408, -2442, 7641, -12549, 10094, -3120, 1, -54, 1101, -11010, 58923, -173010, 273625, -215094, 65520
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums of the unsigned triangle = A082480: (1, 2, 4, 12, 48, 288, 2592,...). Right border starting with row 1 (unsigned) = A003266: (1, 1, 2, 6, 30, 240,...).
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FORMULA
| Triangle read by rows, n-th row = n-th degree polynomial as product of (x-F1)*(x-F2)*(x-F3)*...(x-Fn). n-th row = charpoly of an nxn matrix with F1, F2, F3,...Fn as the diagonal and the rest zeros.
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EXAMPLE
| First few rows of the unsigned triangle =
1;
1, 1;
1, 2, 1;
1, 4, 5, 2;
1, 7, 17, 17, 6;
1, 12, 52, 102, 91, 30;
1, 20, 148, 518, 907, 758, 240;
1, 33, 408, 2442, 7641, 12549, 10094, 3120;
1, 54, 1101, 11010, 58923, 173010, 273623, 215094, 65520;
...
Example: row 5 as a signed polynomial = x^5 - 12x^4 + 52x^3 - 102x^2 + 91x - 30.
= (x-1)*(x-1)*(x-2)*(x-3)*(x-5)
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CROSSREFS
| A000045, A082480, A003266
Sequence in context: A057785 A192404 A158471 * A198895 A118686 A102610
Adjacent sequences: A158469 A158470 A158471 * A158473 A158474 A158475
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KEYWORD
| tabl,sign
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 20 2009
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