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 A146966 ((6+sqrt7)^n+(6-sqrt7))^n/2 1
 1, 6, 43, 342, 2857, 24366, 209539, 1807854, 15617617, 134983638, 1166892763, 10088187654, 87218361721, 754062898686, 6519422294323, 56365243469982, 487319675104417, 4213244040623526, 36426657909454219, 314935817735368374 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA 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] EXAMPLE a(3)=342 PROG (MAGMA) Z:= PolynomialRing(Integers()); N:=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] CROSSREFS Sequence in context: A153397 A005786 A071541 * A220097 A090010 A176732 Adjacent sequences:  A146963 A146964 A146965 * A146967 A146968 A146969 KEYWORD nonn AUTHOR Al Hakanson (hawkuu(AT)gmail.com), Nov 03 2008 EXTENSIONS Extended beyond a(7) by Klaus Brockhaus, Nov 05 2008 STATUS approved

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