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Search: id:A154245
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| A154245 |
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a(n) = ((4+sqrt(7))^n-(4-sqrt(7))^n)/(2*sqrt(7)). |
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+0
1
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| 1, 8, 55, 368, 2449, 16280, 108199, 719072, 4778785, 31758632, 211059991, 1402652240, 9321678001, 61949553848, 411701328775, 2736064645568, 18183205205569, 120841059834440, 803079631825399, 5337067516093232
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Second binomial transform of A109115.
lim_{n -> infinity} a(n)/a(n-1) = 4+sqrt(7) = 6.6457513110....
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FORMULA
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a(n) = 8*a(n-1)-9*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-8x+9x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 06 2009]
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PROGRAM
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-7); S:=[ ((4+r)^n-(4-r)^n)/(2*r): n in [1..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 07 2009]
(Other) Sage: [lucas_number1(n, 8, 9) for n in xrange(1, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
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Equals (A094432 without initial term 0)/3.
Cf. A010465 (decimal expansion of square root of 7), A109115.
Sequence in context: A026994 A110184 A013698 this_sequence A143420 A075734 A033890
Adjacent sequences: A154242 A154243 A154244 this_sequence A154246 A154247 A154248
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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 05 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jan 07 2009
Edited by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 06 2009
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