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A164608
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Expansion of (1+4*x)/(1-8*x+8*x^2).
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3
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1, 12, 88, 608, 4160, 28416, 194048, 1325056, 9048064, 61784064, 421888000, 2880831488, 19671547904, 134325731328, 917233467392, 6263261888512, 42768227368960, 292039723843584, 1994171971796992, 13617057983627264
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A054490. Fourth binomial transform of A164683. Inverse binomial transform of A164609.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..149 from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (8,-8).
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FORMULA
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a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 12.
a(n) = A057084(n) + 4*A057084(n-1).
a(n) = ((2+4*sqrt(2))*(4+2*sqrt(2))^n + (2-4*sqrt(2))*(4-2*sqrt(2))^n)/4.
E.g.f.: exp(4*x)*(cosh(2*sqrt(2)*x) + 2*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 10 2017
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MAPLE
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a:=series((1+4*x)/(1-8*x+8*x^2), x=0, 20): seq(coeff(a, x, n), n=0..19); # Paolo P. Lava, Mar 28 2019
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MATHEMATICA
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LinearRecurrence[{8, -8}, {1, 12, 88}, 50] (* G. C. Greubel, Aug 10 2017 *)
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PROG
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(MAGMA) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((2+4*r)*(4+2*r)^n+(2-4*r)*(4-2*r)^n)/4: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 22 2009
(PARI) x='x+O('x^50); Vec((1+4*x)/(1-8*x+8*x^2)) \\ G. C. Greubel, Aug 10 2017
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CROSSREFS
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Cf. A054490, A164683, A164609.
Sequence in context: A178257 A057406 A125349 * A081009 A155635 A126507
Adjacent sequences: A164605 A164606 A164607 * A164609 A164610 A164611
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KEYWORD
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nonn,easy
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AUTHOR
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Al Hakanson (hawkuu(AT)gmail.com), Aug 17 2009
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EXTENSIONS
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Edited and extended beyond a(5) by Klaus Brockhaus, Aug 22 2009
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STATUS
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approved
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