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A155464
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a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 0, a(1) = 51, a(2) = 340.
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5
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0, 51, 340, 2023, 11832, 69003, 402220, 2344351, 13663920, 79639203, 464171332, 2705388823, 15768161640, 91903581051, 535653324700, 3122016367183, 18196444878432, 106056652903443, 618143472542260, 3602804182350151
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OFFSET
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0,2
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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) = 0, a(1) = 51.
a(n) = ((1+sqrt(2))*(3+2*sqrt(2))^n + (1-sqrt(2))*(3-2*sqrt(2))^n -2)*(17/4).
G.f.: 17*x*(3-x)/((1-x)*(1-6*x+x^2)).
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MATHEMATICA
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LinearRecurrence[{7, -7, 1}, {0, 51, 340}, 30] (* Harvey P. Dale, Jun 10 2013 *)
Table[17*(LucasL[2*n+1, 2] - 2)/4, {n, 0, 50}] (* G. C. Greubel, Aug 21 2018 *)
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PROG
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(PARI) {m=20; v=concat([0, 51, 340], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}
(Magma) I:=[0, 51, 340]; [n le 3 select I[n] else 7*Self(n-1) - 7*Self(n-2) + Self(n-3): n in [1..30]]; // 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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