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A147958
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((7+sqrt2)^n+(7-sqrt2)^n)/2
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2
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1, 7, 51, 385, 2993, 23807, 192627, 1577849, 13036417, 108350935, 904201491, 7566326929, 63431106929, 532418131343, 4472591813139, 37592633210825, 316085049734017, 2658336935367463, 22360719757645683, 188108240644768801
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 7th binomial transform of A077957 . Binomial transform of A147957 . Inverse binomial transform of A147959 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 30 2008]
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FORMULA
| a(n)=14*a(n-1)-47*a(n-2), n>1 ; a(0)=1, a(1)=7 . G.f.: (1-7x)/(1-14x+47x^2). a(n)=(Sum_{k, 0<=k<=n} A098158(n,k)*7^(2k)*2^(n-k))/7^n. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 19 2008]
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EXAMPLE
| a(3)=385
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PROG
| (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r2>:=NumberField(x^2-2); S:=[ ((7+r2)^n+(7-r2)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 19 2008]
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CROSSREFS
| Sequence in context: A015555 A137382 A162757 * A104454 A019472 A081216
Adjacent sequences: A147955 A147956 A147957 * A147959 A147960 A147961
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Nov 17 2008
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EXTENSIONS
| Extended beyond a(6) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 19 2008
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