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Search: id:A152261
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| A152261 |
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((9+sqrt5)^n+(9-sqrt5)^n)/2 |
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+0
2
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| 1, 9, 86, 864, 9016, 96624, 1054016, 11628864, 129214336, 1442064384, 16136869376, 180866755584, 2029199527936, 22779718078464, 255815761289216, 2873425129242624, 32279654468386816, 362653470608523264
(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 A152109. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2008]
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FORMULA
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a(n)=18*a(n-1)-76*a(n-2), n>1 ; a(0)=1, a(1)=9. G.f.: (1-9*x)/(1-18*x+76*x^2). a(n)=Sum{k, 0<=k<=n}A098158(n,k)*9^(2k-n)*5^(n-k). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 03 2008]
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EXAMPLE
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a(3)=864
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PROGRAM
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r5>:=NumberField(x^2-5); S:=[ ((9+r5)^n+(9-r5)^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: A142982 A029711 A015581 this_sequence A028339 A100814 A055725
Adjacent sequences: A152258 A152259 A152260 this_sequence A152262 A152263 A152264
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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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