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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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1
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Fourth binomial transform of A162255.
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FORMULA
| 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).
Contribution from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009: (Start)
G.f.=(3-10x)/(1-8x+14x^2).
Rec. rel.: a(n)=8a(n-1)-14a(n-2); a(0)=3, a(1)=14.
(End)
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MAPLE
| seq(simplify(((3+sqrt(2))*(4+sqrt(2))^n+(3-sqrt(2))*(4-sqrt(2))^n)*1/2), n = 0 .. 20); [From Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009]
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PROG
| (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] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 01 2009]
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CROSSREFS
| Cf. A162255, A161940 (Fifth binomial transform of A162255).
Sequence in context: A020065 A028938 A038213 * A001579 A006772 A009020
Adjacent sequences: A161936 A161937 A161938 * A161940 A161941 A161942
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Jun 22 2009
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EXTENSIONS
| Definition corrected by Emeric Deutsch, Jun 28 2009
Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 01 2009
Extended by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 28 2009
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