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Search: id:A133209
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| A133209 |
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a(n) = 4a(n-1)-6a(n-2)+4a(n-3), n > 3; a(0) = 3, a(1) = 2, a(2) = a(3) = 0. |
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+0
2
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| 3, 2, 0, 0, 8, 32, 80, 160, 288, 512, 960, 1920, 3968, 8192, 16640, 33280, 66048, 131072, 261120, 522240, 1046528, 2097152, 4198400, 8396800, 16785408, 33554432, 67092480, 134184960, 268402688, 536870912, 1073807360, 2147614720
(list; graph; listen)
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OFFSET
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0,1
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FORMULA
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Sequence is identical to its fourth differences.
a(n)=2^n + 2^[(n+3)/2]*cos((n+1)Pi/4); a(n)=2^n + (1+i)^(n+1) + (1-i)^(n+1), where i=sqrt(-1). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2007
G.f.: -(3-10*x+10*x^2)/(2*x-1)/(2*x^2-2*x+1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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MAPLE
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a[0]:=3: a[1]:=2: a[2]:=0: a[3]:=0; for n from 4 to 27 do a[n]:=4*a[n-1]-6*a[n-2]+4*a[n-3] end do: seq(a[n], n=0..27); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2007
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MATHEMATICA
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a = {3, 2, 0, 0}; Do[AppendTo[a, 4*a[[ -1]] - 6*a[[ -2]] + 4*a[[ -3]]], {30}]; a - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Oct 14 2007
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CROSSREFS
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Cf. A131470, A009116, A099087.
Sequence in context: A062707 A160230 A059033 this_sequence A144553 A131290 A116604
Adjacent sequences: A133206 A133207 A133208 this_sequence A133210 A133211 A133212
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KEYWORD
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nonn,easy
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Oct 11 2007
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 14 2007
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