

A084132


a(n) = 4a(n1) + 6a(n2), a(0)=1, a(1)=2.


3



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

0,2


COMMENTS

Binomial transform of A002535.


LINKS

Table of n, a(n) for n=0..21.
Index entries for linear recurrences with constant coefficients, signature (4,6).


FORMULA

a(n) = (2+sqrt(10))^n/2 + (2sqrt(10))^n/2.
G.f.: (12x)/(14x6x^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*k2)/(x*(5*k+3)  1/G(k+1))); (continued fraction).  Sergei N. Gladkovskii, Jun 03 2013


PROG

(Sage) [lucas_number2(n, 4, 6)/2 for n in range(0, 22)] # Zerinvary Lajos, May 14 2009


CROSSREFS

Cf. A005667.
Sequence in context: A197777 A197608 A325925 * A271235 A084770 A086243
Adjacent sequences: A084129 A084130 A084131 * A084133 A084134 A084135


KEYWORD

easy,nonn,changed


AUTHOR

Paul Barry, May 16 2003


STATUS

approved



