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A167375
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a(n)=3*a(n-1)-a(n-2) with a(0)=1, a(1)=3, a(2)=11.
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2
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1, 3, 11, 30, 79, 207, 542, 1419, 3715, 9726, 25463, 66663, 174526, 456915, 1196219, 3131742, 8199007, 21465279, 56196830, 147125211, 385178803, 1008411198, 2640054791, 6911753175, 18095204734, 47373861027, 124026378347, 324705274014, 850089443695
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: (3*x^2+1)/(1-3*x+x^2).
a(n) = 3*L(2n+1)-F(2n), where F(n) is the n-th Fibonacci number and L(n) is the n-th Lucas number. - Rigoberto Florez, Dec 24 2018
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MATHEMATICA
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Join[{1}, LinearRecurrence[{3, -1}, {3, 11}, 30]] (* Harvey P. Dale, Jun 25 2014 *)
CoefficientList[Series[(3 x^2 + 1)/(1 - 3 x + x^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jun 26 2014 *)
Table[3LucasL[2n+1]-Fibonacci[2n], {n, 0, 20}] (* Rigoberto Florez, Dec 24 2018 *)
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PROG
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(Magma) I:=[1, 3, 11]; [n le 3 select I[n] else 3*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jun 26 2014
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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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STATUS
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approved
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