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A147689
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((7+sqrt8)^n+(7-sqrt8)^n)/2
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1
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1, 7, 57, 511, 4817, 46487, 453321, 4440527, 43581217, 428075431, 4206226137, 41336073247, 406249753841, 3992717550647, 39241805801577, 385683861645551, 3790660025173057, 37256202024955207, 366169767317277561
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n)=14*a(n-1)-41*a(n-2), a(0)=1, a(1)=7. G.f.: (1-7x)/(1-14x+41x^2). a(n)=(Sum_{k, 0<=k<=n}A098158(n,k)*7^(2k)*8^(n-k))/7^n. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 13 2008]
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EXAMPLE
| a(3)=511
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PROG
| (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r8>:=NumberField(x^2-8); S:=[ ((7+r8)^n+(7-r8)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 13 2008]
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CROSSREFS
| Sequence in context: A082413 A142990 A202250 * A176733 A062192 A122649
Adjacent sequences: A147686 A147687 A147688 * A147690 A147691 A147692
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Nov 10 2008
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EXTENSIONS
| Extended beyond a(6) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 13 2008
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