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A164603
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((1+4*sqrt(2))*(2+2*sqrt(2))^n+(1-4*sqrt(2))*(2-2*sqrt(2))^n)/2.
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3
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1, 18, 76, 376, 1808, 8736, 42176, 203648, 983296, 4747776, 22924288, 110688256, 534450176, 2580553728, 12460015616, 60162277376, 290489171968, 1402605797376, 6772379877376, 32699942699008, 157889290305536
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A164602. Second binomial transform of A164702. Inverse binomial transform of A164604.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..164
Index to sequences with linear recurrences with constant coefficients, signature (4,4).
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FORMULA
| a(n) = 4*a(n-1)+4*a(n-2) for n > 1; a(0) = 1, a(1) = 18.
G.f.: (1+14*x)/(1-4*x-4*x^2).
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MATHEMATICA
| CoefficientList[Series[(-1-14 n)/(-1+4 n+4 n^2), {n, 0, 20}], n] (* From Harvey P. Dale, Feb 22, 2011 *)
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PROG
| (MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+4*r)*(2+2*r)^n+(1-4*r)*(2-2*r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 23 2009]
(PARI) Vec((1+14*x)/(1-4*x-4*x^2)+O(x^99)) \\ Charles R Greathouse IV, Jun 12 2011
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CROSSREFS
| Cf. A164602, A164702, A164604.
Sequence in context: A022145 A143666 A139757 * A100187 A197886 A039453
Adjacent sequences: A164600 A164601 A164602 * A164604 A164605 A164606
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KEYWORD
| nonn,easy
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AUTHOR
| Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
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EXTENSIONS
| Edited and extended beyond a(5) by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Aug 23 2009
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