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Search: id:A154597
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| A154597 |
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a(n) = ((15+sqrt(229))^n-(15-sqrt(229))^n)/(2^n*sqrt(229)). |
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+0
3
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| 1, 15, 226, 3405, 51301, 772920, 11645101, 175449435, 2643386626, 39826248825, 600037119001, 9040383033840, 136205782626601, 2052127122432855, 30918112619119426, 465823816409224245, 7018275358757483101
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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lim_{n -> infinity} a(n)/a(n-1) = 1/(imaginary part of (15+2*I)^(1/2))^2 = 15.0663729752.... [From Klaus Brockhaus, Oct 07 2009]
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FORMULA
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G.f.: x/(1-15*x-x^2). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009, corrected Oct 07 2009]
a(n) = 15*a(n-1)+a(n-2)for n>1; a(0)=0, a(1)=1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 12 2009]
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MATHEMATICA
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a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*15, {n, 3*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 27 2009]
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-229); S:=[ ((15+r)^n-(15-r)^n)/(2^n*r): n in [1..17] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 12 2009]
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CROSSREFS
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First bisection is A098247.
Cf. A166125 (decimal expansion of sqrt(229)), A166126 (decimal expansion of 1/(imaginary part of (15+2*I)^(1/2))^2).
Sequence in context: A001024 A012643 A067222 this_sequence A041422 A129836 A075262
Adjacent sequences: A154594 A154595 A154596 this_sequence A154598 A154599 A154600
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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), Jan 12 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de) and Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 12 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 07 2009
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