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A122069
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a(n) = 3*a(n-1) + 9*a(n-2) for n > 1, with a(0)=1, a(1)=3.
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3
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1, 3, 18, 81, 405, 1944, 9477, 45927, 223074, 1082565, 5255361, 25509168, 123825753, 601059771, 2917611090, 14162371209, 68745613437, 333698181192, 1619805064509, 7862698824255, 38166342053346, 185263315578333
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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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a(n) = 3^n*Fibonacci(n+1) = 3^n*A000045(n+1).
a(n) = Sum_{k=0..n} 2^k*A016095(n,k).
G.f.: 1/(1-3*x-9*x^2).
a(n+1)/a(n) -> 3*((1+sqrt(5))/2 if n ->infinity.
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MAPLE
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with(combinat); seq(3^n*fibonacci(n+1), n=0..25); # G. C. Greubel, Oct 03 2019
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MATHEMATICA
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Table[3^n*Fibonacci[n+1], {n, 0, 25}] (* G. C. Greubel, Oct 03 2019 *)
LinearRecurrence[{3, 9}, {1, 3}, 30] (* Harvey P. Dale, Apr 28 2020 *)
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PROG
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(Sage) [lucas_number1(n, 3, -9) for n in range(1, 23)] # Zerinvary Lajos, Apr 22 2009
(PARI) vector(26, n, 3^(n-1)*fibonacci(n) ) \\ G. C. Greubel, Oct 03 2019
(Magma) [3^n*Fibonacci(n+1): n in [0..25]]; // G. C. Greubel, Oct 03 2019
(GAP) List([0..25], n-> 3^n*Fibonacci(n+1) ); # G. C. Greubel, Oct 03 2019
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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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