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A167816
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Numerator of x(n) = x(n-1) + x(n-2), x(0)=0, x(1)=1/3; denominator=A167817.
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7
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0, 1, 1, 2, 1, 5, 8, 13, 7, 34, 55, 89, 48, 233, 377, 610, 329, 1597, 2584, 4181, 2255, 10946, 17711, 28657, 15456, 75025, 121393, 196418, 105937, 514229, 832040, 1346269, 726103, 3524578, 5702887, 9227465, 4976784, 24157817, 39088169, 63245986, 34111385
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OFFSET
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0,4
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LINKS
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FORMULA
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a(4*n) = A004187(n) = (a(4*n-1) + a(4*n-2))/3;
a(4*n+1) = A033889(n) = 3*a(4*n-1) + a(4*n-2);
a(4*n+2) = A033890(n) = a(4*n-1) + 3*a(4*n-2);
a(4*n+3) = A033891(n) = a(4*n-1) + a(4*n-2).
Numerator of Fibonacci(n) / Fibonacci(2n-4) for n>=3. - Gary Detlefs, Dec 20 2010
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MATHEMATICA
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Numerator[LinearRecurrence[{1, 1}, {0, 1/3}, 40]] (* Harvey P. Dale, Dec 07 2014 *)
LinearRecurrence[{0, 0, 0, 7, 0, 0, 0, -1}, {0, 1, 1, 2, 1, 5, 8, 13}, 39] (* Ray Chandler, Aug 03 2015 *)
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PROG
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(Magma) [0, 1, 1] cat [Numerator(Fibonacci(n)/Fibonacci(2*n-4)): n in [3..40]]; // Vincenzo Librandi, Jun 28 2016
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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