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A155465
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a(n) = 7*a(n-1) - 7*a(n-2) + a(n-3) for n > 2; a(0) = 7, a(1) = 88, a(2) = 555.
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5
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7, 88, 555, 3276, 19135, 111568, 650307, 3790308, 22091575, 128759176, 750463515, 4374021948, 25493668207, 148587987328, 866034255795, 5047617547476, 29419671029095, 171470408627128, 999402780733707, 5824946275775148
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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) = 7, a(1) = 88.
a(n) = ((31+25*sqrt(2))*(3+2*sqrt(2))^n + (31-25*sqrt(2))*(3-2*sqrt(2))^n - 34)/4.
G.f.: (7+39*x-12*x^2)/((1-x)*(1-6*x+x^2)).
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MATHEMATICA
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LinearRecurrence[{7, -7, 1}, {7, 88, 555}, 30] (* Harvey P. Dale, Apr 29 2012 *)
Table[(3*LucasL[2*n+3, 2] + 10*LucasL[2*n+1, 2] - 34)/4, {n, 0, 50}] (* G. C. Greubel, Aug 21 2018 *)
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PROG
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(PARI) {m=20; v=concat([7, 88, 555], vector(m-3)); for(n=4, m, v[n]=7*v[n-1]-7*v[n-2]+v[n-3]); v}
(Magma) I:=[7, 88, 555]; [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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