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A155466
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a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 28, a(1) = 207, a(2) = 1248.
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5
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28, 207, 1248, 7315, 42676, 248775, 1450008, 8451307, 49257868, 287095935, 1673317776, 9752810755, 56843546788, 331308470007, 1931007273288, 11254735169755, 65597403745276, 382329687301935, 2228380720066368
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OFFSET
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0,1
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COMMENTS
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lim_{n -> infinity} a(n+1)/a(n) = 3+2*sqrt(2).
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LINKS
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FORMULA
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a(n) = 6*a(n-1) - a(n-2) + 34 for n > 1; a(0) = 28, a(1) = 207.
a(n) = ((73+53*sqrt(2))*(3+2*sqrt(2))^n + (73-53*sqrt(2))*(3-2*sqrt(2))^n - 34)/4.
G.f.: (28+11*x-5*x^2)/((1-x)*(1-6*x+x^2)).
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MATHEMATICA
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Table[(10*LucasL[2*n+3, 2] + 3*LucasL[2*n+1, 2] -34)/4, {n, 0, 50}] (* or *) LinearRecurrence[{7, -7, 1}, {28, 207, 1248}, 50] (* G. C. Greubel, Aug 21 2018 *)
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PROG
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(PARI) {m=19; v=concat([28, 207, 1248], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}
(Magma) I:=[28, 207, 1248]; [n le 3 select I[n] else 7*Self(n-1) - 7*Self(n-2) + Self(n-3): n in [1..50]]; // G. C. Greubel, Aug 21 2018
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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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EXTENSIONS
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Comment and recursion formula added, cross-references edited by Klaus Brockhaus, Sep 23 2009
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STATUS
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approved
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