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A033891
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a(n) = Fibonacci(4*n+3).
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18
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2, 13, 89, 610, 4181, 28657, 196418, 1346269, 9227465, 63245986, 433494437, 2971215073, 20365011074, 139583862445, 956722026041, 6557470319842, 44945570212853, 308061521170129, 2111485077978050
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OFFSET
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0,1
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LINKS
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FORMULA
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a(n) = Fibonacci(2*n+2)^2 + Fibonacci(2*n+1)^2. - Gary Detlefs, Oct 12 2011
Let n ** m = n*m + floor(phi*n)*floor(phi*m), where phi = (1 + sqrt(5))/2, denote the Porta-Stolarsky star product of the integers n and m (see A101858). Then a(n) = 2 ** 2 ** ... ** 2 (n+1 factors).
a(2*n+1) = a(n) ** a(n) = Fibonacci(8*n+7); a(3*n+2) = a(n) ** a(n) ** a(n) = Fibonacci(12*n+11) and so on. (End)
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MATHEMATICA
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LinearRecurrence[{7, -1}, {2, 13}, 31] (* or *) CoefficientList[Series[ (2-x)/(1-7x+x^2), {x, 0, 30}], x] (* Harvey P. Dale, May 03 2011 *)
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PROG
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(Sage) [fibonacci(4*n+3) for n in (0..30)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..30], n-> Fibonacci(4*n+3)); # G. C. Greubel, Jul 14 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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STATUS
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approved
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