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A066258
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Fibonacci(n)^2 * Fibonacci(n+1).
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8
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0, 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; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| D. Zeitlin, Generating Functions for Products of Recursive Sequences, Transactions A.M.S., 116, Apr. 1965, p. 304.
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LINKS
| Harry J. Smith, Table of n, a(n) for n = 0..200
Index to sequences with linear recurrences with constant coefficients, signature (3,6,-3,-1).
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FORMULA
| O.g.f.: -x*(-1+x) / ( (x^2+4*x-1)*(x^2-x-1) ).
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)^n*F(n+2)). - Ralf Stephan, Jul 26 2005
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PROG
| (PARI) { for (n=1, 200, a=fibonacci(n)^2 * fibonacci(n+1); write("b066258.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 07 2010]
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CROSSREFS
| Cf. A065563, A066259, A000045, A056570.
First differences of A001655.
Sequence in context: A025495 A028570 A009074 * A123771 A046991 A188982
Adjacent sequences: A066255 A066256 A066257 * A066259 A066260 A066261
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KEYWORD
| nonn,easy
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AUTHOR
| Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 09 2001
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