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A066259
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Fibonacci(n)*Fibonacci(n+1)^2.
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5
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1, 4, 18, 75, 320, 1352, 5733, 24276, 102850, 435655, 1845504, 7817616, 33116057, 140281700, 594243090, 2517253683, 10663258432, 45170286424, 191344405725, 810547906740, 3433536036866, 14544692047439, 61612304237568
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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=1,...,200
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FORMULA
| O.g.f.: (x+x^2)/(1-3x-6x^2+3x^3+x^4).
a(n) = second term from left in M^n * [1 0 0 0] where M = the 4 X 4 upper triangular Pascal's triangle matrix [1 3 3 1 / 1 2 1 0 / 1 1 0 0 / 1 0 0 0]. E.g. a(4) = 75 since M^4 * [1 0 0 0} = [125 75 45 27] = [A056570(5) a(4) A066258(3) A056570(4)]. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 31 2004
a(n) = (1/5) {F(3n+2) - (-1)^nF(n-1) }. - Ralf Stephan, Jul 26 2005
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MATHEMATICA
| First[#]Last[#]^2&/@Partition[Fibonacci[Range[30]], 2, 1] (* From Harvey P. Dale, Mar 4 2011 *)
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PROG
| (PARI) { for (n=1, 200, a=fibonacci(n) * fibonacci(n+1)^2; write("b066259.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Feb 07 2010]
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CROSSREFS
| Cf. A065563, A066258, A000045.
Cf. A056570, A066259.
Sequence in context: A026560 A180140 A037674 * A172159 A084213 A048664
Adjacent sequences: A066256 A066257 A066258 * A066260 A066261 A066262
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KEYWORD
| nonn
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AUTHOR
| Len Smiley (smiley(AT)math.uaa.alaska.edu), Dec 09 2001
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