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A086903
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a(n) = 8a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 8, a(n) = (4+sqrt(15))^n + (4-sqrt(15))^n.
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1
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2, 8, 62, 488, 3842, 30248, 238142, 1874888, 14760962, 116212808, 914941502, 7203319208, 56711612162, 446489578088, 3515205012542, 27675150522248, 217885999165442, 1715412842801288, 13505416743244862, 106327921103157608
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| a(n+1)/a(n) converges to (4+sqrt(15)) = 7.872983... a(0)/a(1)=2/8; a(1)/a(2)=8/62; a(2)/a(3)=62/488; a(3)/a(4)=488/3842; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.127016... = 1/(4+sqrt(15)) = (4-sqrt(15)).
Twice A001091. - John W. Layman (layman(AT)math.vt.edu), Sep 25 2003
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2)
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FORMULA
| G.f.: (2-8*x)/(1-8*x+x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 02 2008]
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EXAMPLE
| a(4) = 3842 = 8a(3) - a(2) = 8*488 - 62 = (4+sqrt(15))^4 + (4-sqrt(15))^4 =
3841.9997397 + 0.0002603 = 3842.
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MATHEMATICA
| a[0] = 2; a[1] = 8; a[n_] := 8a[n - 1] - a[n - 2]; Table[ a[n], {n, 0, 19}] (from Robert G. Wilson v Jan 30 2004)
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PROG
| sage: [lucas_number2(n, 8, 1) for n in range(27)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008
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CROSSREFS
| Cf. A086594, A058316, A006245, A009271.
Sequence in context: A140722 A116976 A132574 * A161566 A192516 A159476
Adjacent sequences: A086900 A086901 A086902 * A086904 A086905 A086906
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KEYWORD
| easy,nonn
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AUTHOR
| Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Sep 21 2003
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