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A164542
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a(n) = 8*a(n-1) - 8*a(n-2) for n > 1; a(0) = 1, a(1) = 16.
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3
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1, 16, 120, 832, 5696, 38912, 265728, 1814528, 12390400, 84606976, 577732608, 3945005056, 26938179584, 183945396224, 1256057733120, 8576898695168, 58566727696384, 399918632009728, 2730815234506752, 18647172819976192
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A164541. Fourth binomial transform of A164675. Inverse binomial transform of A164543.
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LINKS
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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) = 16.
G.f.: (1+8*x)/(1-8*x+8*x^2).
a(n) = ((1+3*sqrt(2))*(4+2*sqrt(2))^n + (1-3*sqrt(2))*(4-2*sqrt(2))^n)/2.
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MATHEMATICA
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LinearRecurrence[{8, -8}, {1, 16}, 30] (* Harvey P. Dale, Jul 23 2018 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+3*r)*(4+2*r)^n+(1-3*r)*(4-2*r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 20 2009
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CROSSREFS
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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 15 2009
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EXTENSIONS
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STATUS
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approved
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