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A162563 a(n) = ((5+sqrt(3))*(2+sqrt(3))^n + (5-sqrt(3))*(2-sqrt(3))^n)/2. 3
5, 13, 47, 175, 653, 2437, 9095, 33943, 126677, 472765, 1764383, 6584767, 24574685, 91713973, 342281207, 1277410855, 4767362213, 17792037997, 66400789775, 247811121103, 924843694637, 3451563657445, 12881410935143, 48074080083127 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Binomial transform of A162562. Second binomial transform of A162813. Inverse binomial transform of A162814.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-1).

FORMULA

a(n) = 4*a(n-1) - a(n-2) for n > 1; a(0) = 5, a(1) = 13.

G.f.: (5-7*x)/(1-4*x+x^2).

a(n) = 4*a(n-1) - a(n-2), with a(0)=5 and a(1)=13. - Paolo P. Lava, Jul 15 2009

MATHEMATICA

LinearRecurrence[{4, -1}, {5, 13}, 30] (* Harvey P. Dale, Aug 25 2014 *)

PROG

(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((5+r)*(2+r)^n+(5-r)*(2-r)^n)/2: n in [0..25] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 14 2009

CROSSREFS

Cf. A162562, A162813, A162814.

Sequence in context: A152925 A304964 A120790 * A250133 A025545 A146152

Adjacent sequences:  A162560 A162561 A162562 * A162564 A162565 A162566

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009

EXTENSIONS

Edited and extended beyond a(5) by Klaus Brockhaus, Jul 18 2009

STATUS

approved

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Last modified July 17 20:45 EDT 2019. Contains 325109 sequences. (Running on oeis4.)