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A147961 ((6+sqrt3)^n+(6-sqrt3)^n/2 1
1, 6, 39, 270, 1953, 14526, 109863, 838998, 6442497, 49623030, 382873959, 2956927518, 22848289569, 176600866734, 1365216845031, 10554773538150, 81605126571777, 630953992102374, 4878478728359847, 37720263000939822 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(n)=12*a(n-1)-33*a(n-2), n>1 ; a(0)=1, a(1)=6 . G.f.: (1-6x)/(1-12x+33x^2). a(n)=(Sum_{k, 0<=k<=n} A098158(n,k)*6^(2k)*3^(n-k))/6^n. [From Philippe Deléham, Nov 19 2008]

EXAMPLE

a(3)=270

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r3>:=NumberField(x^2-3); S:=[ ((6+r3)^n+(6-r3)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Nov 19 2008]

CROSSREFS

Sequence in context: A006256 A052392 A199491 * A068765 A006633 A153392

Adjacent sequences:  A147958 A147959 A147960 * A147962 A147963 A147964

KEYWORD

nonn

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008

EXTENSIONS

Extended beyond a(6) by Klaus Brockhaus, Nov 19 2008

STATUS

approved

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Last modified July 29 14:20 EDT 2014. Contains 245039 sequences.