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A162272
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a(n) = ((1+sqrt(3))*(5+sqrt(3))^n + (1-sqrt(3))*(5-sqrt(3))^n)/2.
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4
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1, 8, 58, 404, 2764, 18752, 126712, 854576, 5758096, 38780288, 261124768, 1758081344, 11836068544, 79682895872, 536435450752, 3611330798336, 24311728066816, 163668003104768, 1101822013577728, 7417524067472384, 49935156376013824, 336166034275745792, 2263086902485153792
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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G.f.: (1 - 2*x)/(1 - 10*x + 22*x^2).
a(n) = 10*a(n-1) - 22*a(n-2) for n >= 2; a(0)=1, a(1)=8. (End)
E.g.f.: exp(5*x)*(cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x)). - Stefano Spezia, Dec 31 2022
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MAPLE
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seq(expand(((1+sqrt(3))*(5+sqrt(3))^n+(1-sqrt(3))*(5-sqrt(3))^n)*1/2), n = 0 .. 20); # Emeric Deutsch, Jul 05 2009
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MATHEMATICA
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((1+r)*(5+r)^n+(1-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 02 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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