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A161939
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a(n) = ((3+sqrt(2))*(4+sqrt(2))^n + (3-sqrt(2))*(4-sqrt(2))^n)/2.
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2
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3, 14, 70, 364, 1932, 10360, 55832, 301616, 1631280, 8827616, 47783008, 258677440, 1400457408, 7582175104, 41050997120, 222257525504, 1203346244352, 6515164597760, 35274469361152, 190983450520576, 1034025033108480
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OFFSET
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0,1
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COMMENTS
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Fourth binomial transform of A162255.
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - 14*a(n-2) for n > 1; a(0) = 3; a(1) = 14.
G.f.: (3-10*x)/(1-8*x+14*x^2).
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MAPLE
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seq(simplify(((3+sqrt(2))*(4+sqrt(2))^n+(3-sqrt(2))*(4-sqrt(2))^n)*1/2), n = 0 .. 20); # Emeric Deutsch, Jun 28 2009
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MATHEMATICA
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LinearRecurrence[{8, -14}, {3, 14}, 30] (* Harvey P. Dale, May 10 2012 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 01 2009
(GAP) a := [3, 14];; for n in [3..10^2] do a[n] := 8*a[n-1] - 14*a[n-2]; od; a; # Muniru A Asiru, Feb 02 2018
(PARI) x='x+O('x^30); Vec((3-10*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Aug 17 2018
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CROSSREFS
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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), Jun 22 2009
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EXTENSIONS
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STATUS
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approved
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