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A163615
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a(n) = ((1+3*sqrt(2))*(4+sqrt(2))^n+(1-3*sqrt(2))*(4-sqrt(2))^n)/2.
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3
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1, 10, 66, 388, 2180, 12008, 65544, 356240, 1932304, 10471072, 56716320, 307135552, 1663055936, 9004549760, 48753614976, 263965223168, 1429171175680, 7737856281088, 41894453789184, 226825642378240, 1228082785977344
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A163614. Fourth binomial transform of A163864. Inverse binomial transform of A163616.
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FORMULA
| a(n) = 8*a(n-1)-14*a(n-2) for n > 1; a(0) = 1, a(1) = 10.
G.f.: (1+2*x)/(1-8*x+14*x^2).
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PROG
| (MAGMA) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(4+r)^n+(1-3*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), Aug 06 2009]
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CROSSREFS
| Cf. A163614, A163864, A163616.
Sequence in context: A026853 A177452 A033504 * A117305 A108275 A086443
Adjacent sequences: A163612 A163613 A163614 * A163616 A163617 A163618
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KEYWORD
| nonn
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
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EXTENSIONS
| Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 06 2009
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