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Search: id:A163072
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| A163072 |
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a(n) = ((4+sqrt(5))*(5+sqrt(5))^n+(4-sqrt(5))*(5-sqrt(5))^n)/2. |
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+0
2
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| 4, 25, 170, 1200, 8600, 62000, 448000, 3240000, 23440000, 169600000, 1227200000, 8880000000, 64256000000, 464960000000, 3364480000000, 24345600000000, 176166400000000, 1274752000000000, 9224192000000000, 66746880000000000
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Binomial transform of A108404 without initial 1. Fifth binomial transform of A163141.
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FORMULA
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a(n) = 10*a(n-1)-20*a(n-2) for n > 1; a(0) = 4, a(1) = 25.
G.f.: (4-15*x)/(1-10*x+20*x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((4+r)*(5+r)^n+(4-r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 21 2009]
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CROSSREFS
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Cf. A108404, A163141.
Sequence in context: A128419 A006880 A081068 this_sequence A140177 A034494 A084210
Adjacent sequences: A163069 A163070 A163071 this_sequence A163073 A163074 A163075
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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), Jul 20 2009
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EXTENSIONS
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Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 21 2009
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