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Search: id:A152265
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| A152265 |
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((8+sqrt7)^n+(8-sqrt7)^n)/2 |
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+0
3
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| 1, 8, 71, 680, 6833, 70568, 739607, 7811336, 82823777, 879934280, 9357993191, 99571637096, 1059740581649, 11280265991912, 120079042716599, 1278289521926600, 13608126915979457, 144867527905855112
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A145302 . Inverse binomial transform of A152266 . [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)-57*a(n-2), n>1 ; a(0)=1, a(1)=8 . G.f.: (1-8*x)/(1-16*x+57*x^2). a(n)=Sum_{k, 0<=k<=n}A098158(n,k)*8^(2k-n)*7^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2008]
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EXAMPLE
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a(3)=680
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r7>:=NumberField(x^2-7); S:=[ ((8+r7)^n+(8-r7)^n)/2: n in [0..17] ]; [ 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: A038145 A015576 A070998 this_sequence A081178 A096341 A075506
Adjacent sequences: A152262 A152263 A152264 this_sequence A152266 A152267 A152268
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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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