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A153884
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a(n) = ((7+sqrt(5))^n-(7-sqrt(5))^n)/(2*sqrt(5)).
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0
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1, 14, 152, 1512, 14480, 136192, 1269568, 11781504, 109080064, 1008734720, 9322763264, 86134358016, 795679428608, 7349600247808, 67884508610560, 627000709644288, 5791091556155392, 53487250561826816, 494013479394738176
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OFFSET
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1,2
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COMMENTS
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Fifth binomial transform of A048878.
lim_{n -> infinity} a(n)/a(n-1) = 7+sqrt(5) = 9.236067977499789696....
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LINKS
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Table of n, a(n) for n=1..19.
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FORMULA
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a(n) = 14*a(n-1)-44*a(n-2) for n>1; a(0)=0, a(1)=1. G.f.: x/(1-14*x+44*x^2). [From Philippe DELEHAM, Jan 03 2009]
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MATHEMATICA
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Join[{a=1, b=14}, Table[c=14*b-44*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 01 2011*)
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PROG
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(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((7+r)^n-(7-r)^n)/(2*r): n in [1..19] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Jan 04 2009]
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CROSSREFS
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Cf. A002163 (decimal expansion of sqrt(5)), A048878.
Sequence in context: A037960 A222677 A016163 * A154239 A016215 A097227
Adjacent sequences: A153881 A153882 A153883 * A153885 A153886 A153887
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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 03 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus, Jan 04 2009
Edited by Klaus Brockhaus, Oct 11 2009
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STATUS
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approved
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