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A124610
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a(n) = 5*a(n-1) + 2*a(n-2), n>1; a(0) = a(1) = 1.
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1
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1, 1, 7, 37, 199, 1069, 5743, 30853, 165751, 890461, 4783807, 25699957, 138067399, 741736909, 3984819343, 21407570533, 115007491351, 617852597821, 3319277971807, 17832095054677, 95799031216999, 514659346194349
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Top left element of powers of the matrix [1,2;3,4].
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FORMULA
| a(n)/a(n-1) tends to (sqrt(33) + 5)/2 = 5.37228132... - Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 03 2008
a(n)=-(1/22)*sqrt(33)*[5/2+(1/2)*sqrt(33)]^n+(1/2)*[5/2-(1/2)*sqrt(33)]^n+(1/22)*[5/2-(1/2) *sqrt(33)]^n*sqrt(33)+(1/2)*[5/2+(1/2)*sqrt(33)]^n, with n>=0 - Paolo P. Lava (paoloplava(AT)gmail.com), Jul 07 2008
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EXAMPLE
| a(5) = 1069 because [1,2;3,4]^5 = [1069,1558;2337,3406]
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MATHEMATICA
| Table[MatrixPower[{{1, 2}, {3, 4}}, n][[1]][[1]], {n, 0, 30}]
Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{2, 5}, #]}]&, {1, 1}, 40]][[1]] (* From Harvey P. Dale, Mar 23 2011 *)
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CROSSREFS
| Cf. A100638.
Sequence in context: A069378 A117130 A002807 * A002683 A126475 A077239
Adjacent sequences: A124607 A124608 A124609 * A124611 A124612 A124613
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KEYWORD
| easy,nonn
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AUTHOR
| Fredrik Johansson (fredrik.johansson(AT)gmail.com), Dec 20 2006
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EXTENSIONS
| Recurrence from Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 03 2008
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