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A162275
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a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 2, a(1) = 13.
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2
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2, 13, 86, 574, 3848, 25852, 173864, 1169896, 7873952, 53001808, 356791136, 2401871584, 16169310848, 108851933632, 732794497664, 4933202436736, 33210545418752, 223575000579328, 1505118006580736, 10132530053062144, 68212704385845248, 459211382691085312
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 2, a(1) = 13.
a(n) = ((2+sqrt(3))*(5+sqrt(3))^n + (2-sqrt(3))*(5-sqrt(3))^n)/2.
G.f.: (2-7*x)/(1-10*x+22*x^2).
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MAPLE
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a := proc (n) options operator, arrow; expand((1/2)*(2+sqrt(3))*(5+sqrt(3))^n+(1/2)*(2-sqrt(3))*(5-sqrt(3))^n) end proc: seq(a(n), n = 0 .. 20); # Emeric Deutsch, Jul 09 2009
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MATHEMATICA
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LinearRecurrence[{10, -22}, {2, 13}, 30] (* Harvey P. Dale, Jun 14 2017 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((2+r)*(5+r)^n+(2-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 05 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
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EXTENSIONS
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STATUS
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approved
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