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Search: id:A162770
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| A162770 |
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a(n) = ((2+sqrt(5))*(1+sqrt(5))^n+(2-sqrt(5))*(1-sqrt(5))^n)/2. |
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+0
2
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| 2, 7, 22, 72, 232, 752, 2432, 7872, 25472, 82432, 266752, 863232, 2793472, 9039872, 29253632, 94666752, 306348032, 991363072, 3208118272, 10381688832, 33595850752, 108718456832, 351820316672, 1138514460672, 3684310188032
(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 A162963. Inverse binomial transform of A001077 without initial 1.
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FORMULA
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a(n) = 2*a(n-1)+4*a(n-2) for n > 1; a(0) = 2, a(1) = 7.
G.f.: (2+3*x)/(1-2*x-4*x^2).
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((2+r)*(1+r)^n+(2-r)*(1-r)^n)/2: n in [0..24] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 19 2009]
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CROSSREFS
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Cf. A162963, A001077.
Sequence in context: A109999 A092690 A030186 this_sequence A116387 A114495 A137398
Adjacent sequences: A162767 A162768 A162769 this_sequence A162771 A162772 A162773
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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 13 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 19 2009
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