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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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8
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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
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OFFSET
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0,1
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COMMENTS
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Pisano period lengths: 1, 1, 8, 1, 6, 8, 48, 2, 24, 6,120, 8, 12, 48, 24, 4, 8, 24, 18, 6, ... . - R. J. Mathar, Aug 10 2012
The Lucas sequence V(1,-4). - Peter Bala, Jun 23 2015
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REFERENCES
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Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001, p. 471.
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LINKS
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FORMULA
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a(n) = [x^n] ( (1 + x + sqrt(1 + 2*x + 17*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015
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MAPLE
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a:= n-> (Matrix([[1, 2]]). Matrix([[1, 1], [4, 0]])^n)[1, 2]:
a := n -> 2*(2*I)^n*ChebyshevT(n, -I/4):
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MATHEMATICA
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Table[2^n*LucasL[n, 1/2], {n, 0, 30}] (* G. C. Greubel, Jan 15 2020 *)
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PROG
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(PARI) polsym(x^2-x-4, 44)
(Sage) [lucas_number2(n, 1, -4) for n in range(0, 27)] # Zerinvary Lajos, Apr 30 2009
(Magma) I:=[2, 1]; [n le 2 select I[n] else Self(n-1) + 4*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 15 2020
(GAP) a:=[2, 1];; for n in [3..30] do a[n]:=a[n-1]+4*a[n-2]; od; a; # G. C. Greubel, Jan 15 2020
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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