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A128535
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F(n)*L(n-2) where F=Fibonacci and L=Lucas numbers.
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4
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0, -1, 2, 2, 9, 20, 56, 143, 378, 986, 2585, 6764, 17712, 46367, 121394, 317810, 832041, 2178308, 5702888, 14930351, 39088170, 102334154, 267914297, 701408732, 1836311904, 4807526975, 12586269026, 32951280098, 86267571273, 225851433716, 591286729880
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Generally, F(n)*L(n+k) = F(2*n + k) + F(k)*(-1)^(n+1):
if k=0 the sequence is A001906, if k=1 it is A081714.
a(n+1) = - A116697(2*n). [Reinhard Zumkeller, Feb 25 2011]
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (2,2,-1).
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FORMULA
| a(n) = F(2*(n-1)) - (-1)^(n+1), assuming F(0)=0 and L(0)=2.
a(n)=2*a(n-1)+2*a(n-2)-a(n-3). G.f.: x*(-1+4*x)/((1+x)*(x^2-3*x+1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 16 2009]
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EXAMPLE
| a(7) = 143 because F(7)*L(5) = 13*11.
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MATHEMATICA
| Table[Fibonacci[i]LucasL[i-2], {i, 0, 30}] {* From Harvey P. Dale, Feb 16 2011 *)
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CROSSREFS
| Cf. A001906, A081714, A128533, A128534.
Sequence in context: A007024 A019223 A192302 * A180753 A205390 A204265
Adjacent sequences: A128532 A128533 A128534 * A128536 A128537 A128538
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KEYWORD
| easy,sign
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AUTHOR
| Axel Harvey (ax(AT)hirsig.ca), Mar 09 2007
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EXTENSIONS
| More terms from Harvey P. Dale, Feb 16 2011
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