A157725 a(n) = Fibonacci(n) + 2.
2, 3, 3, 4, 5, 7, 10, 15, 23, 36, 57, 91, 146, 235, 379, 612, 989, 1599, 2586, 4183, 6767, 10948, 17713, 28659, 46370, 75027, 121395, 196420, 317813, 514231, 832042, 1346271, 2178311, 3524580, 5702889, 9227467, 14930354, 24157819, 39088171, 63245988, 102334157
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..285
- Kwang-Wu Chen, Greatest Common Divisors in Shifted Fibonacci Sequences, J. Int. Seq. 14 (2011) # 11.4.7.
- Tomislav Došlić and Biserka Kolarec, On Log-Definite Tempered Combinatorial Sequences, Mathematics (2025) Vol. 13, Iss. 7, 1179.
- Ivana Jovović and Branko Malešević, Some enumerations of non-trivial composition of the differential operations and the directional derivative, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 1, 28-38.
- Index entries for linear recurrences with constant coefficients, signature (2,0,-1).
Crossrefs
Programs
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Haskell
a157725 = (+ 2) . a000045 a157725_list = 2 : 3 : map (subtract 2) (zipWith (+) a157725_list $ tail a157725_list) -- Reinhard Zumkeller, Jul 30 2013 -
Magma
[ Fibonacci(n) + 2: n in [0..40] ]; // Vincenzo Librandi, Apr 24 2011
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Mathematica
Fibonacci[Range[0, 50]] + 2 (* or *) LinearRecurrence[{2, 0, -1}, {2, 3, 3}, 50] (* Paolo Xausa, Jul 28 2024 *) -
PARI
a(n)=fibonacci(n)+2 \\ Charles R Greathouse IV, Jul 02 2013
Formula
G.f.: -(1+x)*(3*x-2) / ( (x-1)*(x^2+x-1) ). - R. J. Mathar, Aug 08 2012
a(0) = 2, a(1) = 3, a(n) = a(n - 2) + a(n - 1) - 2. - Reinhard Zumkeller, Jul 30 2013
E.g.f.: 2*(exp(x) + exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5)). - Stefano Spezia, Apr 09 2025
Comments