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A163064
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a(n) = ((3+sqrt(5))*(4+sqrt(5))^n + (3-sqrt(5))*(4-sqrt(5))^n)/2.
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3
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3, 17, 103, 637, 3963, 24697, 153983, 960197, 5987763, 37339937, 232854103, 1452093517, 9055353003, 56469795337, 352149479663, 2196028088597, 13694580432483, 85400334485297, 532562291125063, 3321094649662237
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OFFSET
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0,1
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COMMENTS
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Binomial transform of A098648 without initial 1. Fourth binomial transform of A163114. Inverse binomial transform of A163065.
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - 11*a(n-2) for n > 1; a(0) = 3, a(1) = 17.
G.f.: (3-7*x)/(1-8*x+11*x^2).
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MATHEMATICA
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CoefficientList[Series[(3-7*x)/(1-8*x+11*x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{8, -11}, {3, 17}, 30] (* G. C. Greubel, Dec 22 2017 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-5); S:=[ ((3+r)*(4+r)^n+(3-r)*(4-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Jul 21 2009
(Magma) I:=[3, 17]; [n le 2 select I[n] else 8*Self(n-1) - 11*Self(n-2): n in [1..30]]; // G. C. Greubel, Dec 22 2017
(PARI) x='x+O('x^30); Vec((3-7*x)/(1-8*x+11*x^2)) \\ G. C. Greubel, Dec 22 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), Jul 20 2009
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EXTENSIONS
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STATUS
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approved
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