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A072265
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Variant of Lucas numbers: a(n)=a(n-1)+4*a(n-2) starting with a(0)=2 and a(1)=1.
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5
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2, 1, 9, 13, 49, 101, 297, 701, 1889, 4693, 12249, 31021, 80017, 204101, 524169, 1340573, 3437249, 8799541, 22548537, 57746701, 147940849, 378927653, 970691049, 2486401661, 6369165857, 16314772501, 41791435929, 107050525933, 274216269649, 702418373381
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.
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FORMULA
| G.f.: (2-x)/(1-x-4x^2). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 02 2003
a(n) = ((1+sqrt(17))/2)^n + ((1-sqrt(17))/2)^n = 4*A006131(n-1)+A006131(n+1) = A075117(4, n).
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MAPLE
| a := n -> (Matrix([[1, 2]]). Matrix([[1, 1], [4, 0]])^n)[1, 2]; seq (a(n), n=0..26); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 15 2008]
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MATHEMATICA
| CoefficientList[Series[(z - 2)/(4 z^2 + z - 1), {z, 0, 200}], z] (* From Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)
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PROG
| (PARI) a(n)=if(n<0, 0, polsym(4+x-x^2, n)[n+1])
(Other) sage: [lucas_number2(n, 1, -4) for n in xrange(0, 27)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
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CROSSREFS
| Cf. A006131.
Sequence in context: A078623 A099599 A085488 * A192352 A180001 A204371
Adjacent sequences: A072262 A072263 A072264 * A072266 A072267 A072268
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KEYWORD
| easy,nonn
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AUTHOR
| M. Kristof (kristmikl(AT)freemail.hu), Jul 08 2002
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EXTENSIONS
| Edited and extended by Henry Bottomley (se16(AT)btinternet.com), Sep 03 2002
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