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A164591
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a(n) = ((4 + sqrt(18))*(4 + sqrt(8))^n + (4 - sqrt(18))*(4 - sqrt(8))^n)/8 .
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3
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1, 7, 48, 328, 2240, 15296, 104448, 713216, 4870144, 33255424, 227082240, 1550614528, 10588258304, 72301150208, 493703135232, 3371215880192, 23020101959680, 157191088635904, 1073367893409792, 7329414438191104, 50048372358250496
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OFFSET
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0,2
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COMMENTS
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Binomial transform of A001109 without initial 0. Fourth binomial transform of A096886. Inverse binomial transform of A164592.
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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) = 7.
G.f.: (1-x)/(1-8*x+8*x^2).
E.g.f.: (1/4)*exp(4*x)*(4*cosh(2*sqrt(2)*x) + 3*sqrt(2)*sinh(2*sqrt(2)*x)). - G. C. Greubel, Aug 12 2017
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MATHEMATICA
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LinearRecurrence[{8, -8}, {1, 7}, 50] (* G. C. Greubel, Aug 12 2017 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(4+2*r)^n+(4-3*r)*(4-2*r)^n)/8: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Aug 24 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 17 2009
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EXTENSIONS
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STATUS
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approved
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