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A084132
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a(n) = 4a(n-1) + 6a(n-2), a(0)=1, a(1)=2.
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3
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1, 2, 14, 68, 356, 1832, 9464, 48848, 252176, 1301792, 6720224, 34691648, 179087936, 924501632, 4772534144, 24637146368, 127183790336, 656558039552, 3389334900224, 17496687838208, 90322760754176, 466271170045952
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A002535.
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LINKS
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Table of n, a(n) for n=0..21.
Index entries for linear recurrences with constant coefficients, signature (4,6).
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FORMULA
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a(n) = (2+sqrt(10))^n/2 + (2-sqrt(10))^n/2.
G.f.: (1-2x)/(1-4x-6x^2).
E.g.f.: exp(2x)cosh(sqrt(10)x).
a(n) = Sum_{k=0..n} A201730(n,k)*9^k. - Philippe Deléham, Dec 06 2011
G.f.: G(0)/2, where G(k) = 1 + 1/(1 - x*(5*k-2)/(x*(5*k+3) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013
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PROG
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(Sage) [lucas_number2(n, 4, -6)/2 for n in range(0, 22)] # Zerinvary Lajos, May 14 2009
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CROSSREFS
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Cf. A005667.
Sequence in context: A197777 A197608 A325925 * A271235 A084770 A086243
Adjacent sequences: A084129 A084130 A084131 * A084133 A084134 A084135
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, May 16 2003
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STATUS
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approved
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