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Search: id:A152263
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| A152263 |
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((8+sqrt6)^n+(8-sqrt6)^n)/2 |
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+0
3
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| 1, 8, 70, 656, 6436, 64928, 665560, 6883136, 71527696, 745221248, 7774933600, 81176105216, 847871534656, 8857730451968, 92547138221440, 967005845328896, 10104359508418816, 105583413105625088, 1103281758201710080
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OFFSET
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0,2
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COMMENT
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Binomial transform of A152262 . Inverse binomial transform of A152264 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2008]
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FORMULA
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a(n)=16*a(n-1)-58*a(n-2), n>1 ; a(0)=1, a(1)=8 . G.f.: (1-8*x)/(1-16*x+58*x^2). a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*8^(2k-n)*6^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2008]
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EXAMPLE
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a(3)=656
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((8+r6)^n+(8-r6)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 03 2008]
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CROSSREFS
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Sequence in context: A152109 A124152 A056631 this_sequence A142986 A123511 A053729
Adjacent sequences: A152260 A152261 A152262 this_sequence A152264 A152265 A152266
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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), Dec 01 2008
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EXTENSIONS
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Extended beyond a(6) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Dec 03 2008
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