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A020695
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Pisot sequence E(2,3).
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8
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2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040, 1346269, 2178309, 3524578, 5702887, 9227465, 14930352, 24157817, 39088169, 63245986, 102334155, 165580141
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OFFSET
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0,1
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COMMENTS
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LINKS
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FORMULA
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a(n) = Fibonacci(n+3); a(n) = a(n-1) + a(n-2).
a(n) = (2^(-n)*((1-sqrt(5))^n*(-2+sqrt(5))+(1+sqrt(5))^n*(2+sqrt(5))))/sqrt(5). - Colin Barker, Jun 05 2016
E.g.f.: 2*(2*sqrt(5)*sinh(sqrt(5)*x/2) + 5*cosh(sqrt(5)*x/2))*exp(x/2)/5. - Ilya Gutkovskiy, Jun 05 2016
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MATHEMATICA
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LinearRecurrence[{1, 1}, {2, 3}, 40] (* or *) Fibonacci[Range[3, 50]] (* Harvey P. Dale, Nov 22 2012 *)
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PROG
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(PARI) Vec((2+x)/(1-x-x^2) + O(x^40)) \\ Colin Barker, Jun 05 2016
(GAP)
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CROSSREFS
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Subsequence of A000045. See A008776 for definitions of Pisot sequences.
See A000045 for the Fibonacci numbers.
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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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