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A147961
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((6+sqrt3)^n+(6-sqrt3)^n/2
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1
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1, 6, 39, 270, 1953, 14526, 109863, 838998, 6442497, 49623030, 382873959, 2956927518, 22848289569, 176600866734, 1365216845031, 10554773538150, 81605126571777, 630953992102374, 4878478728359847, 37720263000939822
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..19.
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FORMULA
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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 DELEHAM, Nov 19 2008]
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EXAMPLE
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a(3)=270
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PROG
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(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]
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CROSSREFS
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Sequence in context: A006256 A052392 A199491 * A068765 A006633 A153392
Adjacent sequences: A147958 A147959 A147960 * A147962 A147963 A147964
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008
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EXTENSIONS
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Extended beyond a(6) by Klaus Brockhaus, Nov 19 2008
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STATUS
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approved
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