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A154348
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a(n) = 16*a(n-1)-56*a(n-2) for n>1; a(0)=0, a(1)=1.
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1
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1, 16, 200, 2304, 25664, 281600, 3068416, 33325056, 361369600, 3915710464, 42414669824, 459354931200, 4974457389056, 53867442077696, 583309459456000, 6316374594945024, 68396663789584384, 740629643316428800
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OFFSET
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1,2
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COMMENTS
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Third binomial transform of A164609, fourth binomial transform of A164608, fifth binomial transform of A054490, sixth binomial transform of A164607, seventh binomial transform of A083100, eighth binomial transform of A164683.
lim_{n -> infinity} a(n)/a(n-1) = 8+2*sqrt(2) = 10.8284271247....
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..135
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FORMULA
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a(n) = 16*a(n-1)-56*a(n-2) for n>1; a(0)=0, a(1)=1. [From Philippe DELEHAM, Jan 12 2009]
a(n) = ((8+2*sqrt(2))^n-(8-2*sqrt(2))^n)/(4*sqrt(2)).
G.f.: 1/(1-16*x+56*x^2). [From Klaus Brockhaus, Jan 12 2009, corrected Oct 08 2009]
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MATHEMATICA
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Join[{a=1, b=16}, Table[c=16*b-56*a; a=b; b=c, {n, 40}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 08 2011*)
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PROG
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((8+2*r)^n-(8-2*r)^n)/(4*r): n in [1..18] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus, Jan 12 2009]
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CROSSREFS
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Cf. A002193 (decimal expansion of sqrt(2)), A164609, A164608, A054490, A164607, A083100, A164683.
Sequence in context: A081679 A154249 A125451 * A129333 A001810 A016165
Adjacent sequences: A154345 A154346 A154347 * A154349 A154350 A154351
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009
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EXTENSIONS
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Extended beyond a(7) by Klaus Brockhaus, Jan 12 2009
Edited by Klaus Brockhaus, Oct 08 2009
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STATUS
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approved
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