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A164589
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a(n) = ((4 + 3*sqrt(2))*(1 + 2*sqrt(2))^n + (4 - 3*sqrt(2))*(1 - 2*sqrt(2))^n)/8.
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2
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1, 4, 15, 58, 221, 848, 3243, 12422, 47545, 182044, 696903, 2668114, 10214549, 39105896, 149713635, 573168542, 2194332529, 8400844852, 32162017407, 123129948778, 471394019405, 1804697680256, 6909153496347, 26451190754486, 101266455983401, 387691247248204
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = 2*a(n-1) + 7*a(n-2) for n > 1; a(0) = 1, a(1) = 4.
G.f.: (1 + 2*x)/(1 - 2*x - 7*x^2).
E.g.f.: (1/4)*exp(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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CoefficientList[Series[(1+2x)/(1-2x-7x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{2, 7}, {1, 4}, 30] (* Harvey P. Dale, Jun 22 2011 *)
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PROG
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(Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((4+3*r)*(1+2*r)^n+(4-3*r)*(1-2*r)^n)/8: n in [0..23] ]; [ 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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