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Search: id:A066258
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| A066258 |
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Fibonacci(n)^2 * Fibonacci(n+1). |
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+0
6
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| 1, 2, 12, 45, 200, 832, 3549, 14994, 63580, 269225, 1140624, 4831488, 20466953, 86698690, 367262700, 1555747893, 6590256856, 27916771136, 118257348165, 500946152850, 2122041977276, 8989114033297, 38078498156832
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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D. Zeitlin, Generating Functions for Products of Recursive Sequences, Transactions A.M.S., 116, Apr. 1965, p. 304.
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FORMULA
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O.g.f.: (x-x^2)/(1-3x-6x^2+3x^3+x^4).
a(n) = second term from right in M^(n+1) * [1 0 0 0}, where M = the 4 X 4 upper Pascal's triangular matrix [1 3 3 1 / 1 2 1 0 / 1 1 0 0 / 1 0 0 0]. E.g. a(3) = 45 since M^4 * [1 0 0 0] = [125 75 45 27] where 125 = A056570(5), 75 = A066259(4) and 27 = A056570(4). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 31 2004
a(n) = (1/5) {F(3n+1) - (-1)^nF(n+2) }. - Ralf Stephan, Jul 26 2005
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CROSSREFS
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Cf. A065563, A066259, A000045.
Cf. A056570, A066259.
First differences of A001655.
Sequence in context: A025495 A028570 A009074 this_sequence A123771 A046991 A061990
Adjacent sequences: A066255 A066256 A066257 this_sequence A066259 A066260 A066261
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KEYWORD
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nonn
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AUTHOR
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Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 09 2001
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