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A099868
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a(n) = 5*a(n-1) - a(n-2), a(0) = 3, a(1) = 25.
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2
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3, 25, 122, 585, 2803, 13430, 64347, 308305, 1477178, 7077585, 33910747, 162476150, 778470003, 3729873865, 17870899322, 85624622745, 410252214403, 1965636449270, 9417930031947, 45124013710465, 216202138520378, 1035886678891425, 4963231255936747
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OFFSET
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0,1
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LINKS
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A. F. Horadam, Pell Identities, Fib. Quart., Vol. 9, No. 3, 1971, pp. 245-252.
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FORMULA
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a(n) = (2^(-1-n)*((5-sqrt(21))^n*(-35+3*sqrt(21)) + (5+sqrt(21))^n*(35+3*sqrt(21)))) / sqrt(21). - Colin Barker, Mar 28 2017
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MAPLE
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a[0]:=3: a[1]:=25: for n from 2 to 30 do a[n]:=5*a[n-1]-a[n-2] od: seq(a[n], n=0..25);
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MATHEMATICA
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LinearRecurrence[{5, -1}, {3, 25}, 30] (* G. C. Greubel, Nov 20 2018 *)
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PROG
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(PARI) Vec((3+10*x) / (1-5*x+x^2) + O(x^30)) \\ Colin Barker, Mar 28 2017
(Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (3 +10*x)/(1-5*x+x^2))); // G. C. Greubel, Nov 20 2018
(Sage) s=((3+10*x)/(1-5*x+x^2)).series(x, 30); s.coefficients(x, sparse=False) # G. C. Greubel, Nov 20 2018
(GAP) a:=[3, 25];; for n in [3..30] do a[n]:=5*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Nov 20 2018
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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