This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A157725 #38 Apr 09 2025 14:14:36
%S A157725 2,3,3,4,5,7,10,15,23,36,57,91,146,235,379,612,989,1599,2586,4183,
%T A157725 6767,10948,17713,28659,46370,75027,121395,196420,317813,514231,
%U A157725 832042,1346271,2178311,3524580,5702889,9227467,14930354,24157819,39088171,63245988,102334157
%N A157725 a(n) = Fibonacci(n) + 2.
%C A157725 a(n) = A226649(2*n+1) - A226649(2*n). - _Reinhard Zumkeller_, Jul 30 2013
%H A157725 Vincenzo Librandi, <a href="/A157725/b157725.txt">Table of n, a(n) for n = 0..285</a>
%H A157725 Kwang-Wu Chen, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Chen/chen70.html">Greatest Common Divisors in Shifted Fibonacci Sequences</a>, J. Int. Seq. 14 (2011) # 11.4.7.
%H A157725 Tomislav Došlić and Biserka Kolarec, <a href="https://doi.org/10.3390/math13071179">On Log-Definite Tempered Combinatorial Sequences</a>, Mathematics (2025) Vol. 13, Iss. 7, 1179.
%H A157725 Ivana Jovović and Branko Malešević, <a href="http://nntdm.net/volume-23-2017/number-1/28-38/">Some enumerations of non-trivial composition of the differential operations and the directional derivative</a>, Notes on Number Theory and Discrete Mathematics, Vol. 23, 2017, No. 1, 28-38.
%H A157725 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-1).
%F A157725 G.f.: -(1+x)*(3*x-2) / ( (x-1)*(x^2+x-1) ). - _R. J. Mathar_, Aug 08 2012
%F A157725 a(0) = 2, a(1) = 3, a(n) = a(n - 2) + a(n - 1) - 2. - _Reinhard Zumkeller_, Jul 30 2013
%F A157725 E.g.f.: 2*(exp(x) + exp(x/2)*sinh(sqrt(5)*x/2)/sqrt(5)). - _Stefano Spezia_, Apr 09 2025
%t A157725 Fibonacci[Range[0, 50]] + 2 (* or *)
%t A157725 LinearRecurrence[{2, 0, -1}, {2, 3, 3}, 50] (* _Paolo Xausa_, Jul 28 2024 *)
%o A157725 (Magma) [ Fibonacci(n) + 2: n in [0..40] ]; // _Vincenzo Librandi_, Apr 24 2011
%o A157725 (PARI) a(n)=fibonacci(n)+2 \\ _Charles R Greathouse IV_, Jul 02 2013
%o A157725 (Haskell)
%o A157725 a157725 = (+ 2) . a000045
%o A157725 a157725_list = 2 : 3 : map (subtract 2)
%o A157725 (zipWith (+) a157725_list $ tail a157725_list)
%o A157725 -- _Reinhard Zumkeller_, Jul 30 2013
%Y A157725 Cf. A000045, A001611, A000071, A001911, A157726, A006327, A157727, A157728, A157729, A167616, A226649.
%K A157725 nonn,easy
%O A157725 0,1
%A A157725 _N. J. A. Sloane_, Jun 26 2010