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A163610
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a(n) = ((5 + 2*sqrt(2))*(4 + sqrt(2))^n + (5 - 2*sqrt(2))*(4 - sqrt(2))^n)/2.
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4
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5, 24, 122, 640, 3412, 18336, 98920, 534656, 2892368, 15653760, 84736928, 458742784, 2483625280, 13446603264, 72802072192, 394164131840, 2134084044032, 11554374506496, 62557819435520, 338701312393216, 1833801027048448
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OFFSET
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0,1
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COMMENTS
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Binomial transform of A163609. Fourth binomial transform of A163888. Inverse binomial transform of A163611.
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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) = 5, a(1) = 24.
G.f.: (5-16*x)/(1-8*x+14*x^2).
E.g.f.: exp(4*x)*( 5*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - G. C. Greubel, Jul 29 2017
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MATHEMATICA
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LinearRecurrence[{8, -14}, {5, 24}, 30] (* Harvey P. Dale, May 29 2016 *)
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PROG
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(Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+2*r)*(4+r)^n+(5-2*r)*(4-r)^n)/2: n in [0..20] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 06 2009
(PARI) x='x+O('x^50); Vec((5-16*x)/(1-8*x+14*x^2)) \\ G. C. Greubel, Jul 29 2017
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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), Aug 01 2009
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EXTENSIONS
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STATUS
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approved
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