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A146966
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((6+sqrt7)^n+(6-sqrt7))^n/2
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1
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1, 6, 43, 342, 2857, 24366, 209539, 1807854, 15617617, 134983638, 1166892763, 10088187654, 87218361721, 754062898686, 6519422294323, 56365243469982, 487319675104417, 4213244040623526, 36426657909454219, 314935817735368374
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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)-29*a(n-2); a(0)=1, a(1)=6. [From Philippe DELEHAM, Nov 05 2008]
G.f.: (1-6*x)/(1-12*x+29*x^2) [From Klaus Brockhaus, Nov 05 2008]
a(n)=(Sum_{k, 0<=k<=n}A098158(n,k)*6^(2*k)*7^(n-k))/6^n. [From Philippe DELEHAM, Nov 06 2008]
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EXAMPLE
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a(3)=342
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PROG
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((6+r7)^n+(6-r7)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Nov 05 2008]
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CROSSREFS
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Sequence in context: A153397 A005786 A071541 * A220097 A090010 A176732
Adjacent sequences: A146963 A146964 A146965 * A146967 A146968 A146969
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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 03 2008
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008
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STATUS
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approved
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