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A084132 a(n) = 4a(n-1) + 6a(n-2), 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 (list; graph; refs; listen; history; text; internal format)
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 + (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

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

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Last modified December 14 03:31 EST 2019. Contains 329978 sequences. (Running on oeis4.)