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A152055 a(n) = ((8+sqrt3)^n + (8-sqrt3)^n/2. 1
1, 8, 67, 584, 5257, 48488, 455131, 4324328, 41426257, 399036104, 3857575987, 37380013448, 362768079961, 3524108459048, 34256882467147, 333139503472424, 3240562225062817, 31527485889187208, 306765478498163491 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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

FORMULA

From Philippe Deléham, Nov 26 2008: (Start)

a(n) = 16*a(n-1) - 61*a(n-2), n > 1; a(0)=1, a(1)=8.

G.f.: (1-8*x)/(1-16x+61*x^2).

a(n) = (Sum_{k=0..n} A098158(n,k)*8^(2*k)*3^(n-k))/8^n. (End)

EXAMPLE

a(3)=584

MATHEMATICA

LinearRecurrence[{16, -61}, {1, 8}, 30] (* Harvey P. Dale, Sep 02 2018 *)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((8+r3)^n+(8-r3)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Nov 26 2008

CROSSREFS

Sequence in context: A228419 A091645 A015574 * A000434 A304073 A250258

Adjacent sequences:  A152052 A152053 A152054 * A152056 A152057 A152058

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Nov 22 2008

EXTENSIONS

Extended beyond a(6) by Klaus Brockhaus and Philippe Deléham, Nov 26 2008

STATUS

approved

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Last modified June 24 02:02 EDT 2021. Contains 345405 sequences. (Running on oeis4.)