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 A018837 #66 Sep 10 2023 01:42:49
%S A018837 0,3,2,3,2,3,4,5,4,5,6,7,6,7,8,9,8,9,10,11,10,11,12,13,12,13,14,15,14,
%T A018837 15,16,17,16,17,18,19,18,19,20,21,20,21,22,23,22,23,24,25,24,25,26,27,
%U A018837 26,27,28,29,28,29,30,31,30,31,32,33,32,33,34,35,34,35,36,37,36,37,38,39,38,39,40,41,40,41,42,43
%N A018837 Number of steps for knight to reach (n,0) on infinite chessboard.
%C A018837 The knight starts at (0,0) and we count the least number of steps. Row 1 of the array at A065775. - _Clark Kimberling_, Dec 20 2010
%C A018837 Apparently also the minimum number of steps of the (1,3)-leaper to reach (n,n) starting at (0,0). - _R. J. Mathar_, Jan 05 2018
%H A018837 Vincenzo Librandi, <a href="/A018837/b018837.txt">Table of n, a(n) for n = 0..2000</a>
%H A018837 Francis N. Castro, Oscar E. González and Luis A. Medina, <a href="https://doi.org/10.2140/involve.2018.11.127">Generalized exponential sums and the power of computers</a>, Involve, Vol. 11 (2018), Issue 1, pp. 127-142. Also, <a href="http://emmy.uprrp.edu/lmedina/papers/asympgen/index.html">authors' copy</a>.
%H A018837 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,-1).
%F A018837 a(n) = 2[ (n+2)/4 ] if n even, 2[ (n+1)/4 ]+1 if n odd (n >= 8).
%F A018837 G.f.: x*(3-x+x^2-x^3-2*x^4+2*x^5)/((1-x)^2*(1+x)*(1+x^2)). a(n)=A083219(n), n<>1. - _R. J. Mathar_, Dec 15 2008
%F A018837 T(0,0)=0, T(1,0)=3, and for m>=1, T(4m-2,0)=2m, T(4m-1,0)=2m+1, T(4m,0)=2m, T(4m+1,0)=2m+1 where T(.,.) = A065775(.,.). - _Clark Kimberling_, Dec 20 2010
%F A018837 Sum_{n>=1} (-1)^n/a(n) = 5/3 - 2*log(2). - _Amiram Eldar_, Sep 10 2023
%e A018837 a(1)=3 counts these moves: (0,0) to (2,1) to (0,2) to (1,0). - _Clark Kimberling_, Dec 20 2010
%t A018837 CoefficientList[Series[x (3 - x + x^2 - x^3 - 2 x^4 + 2 x^5)/((1-x)^2 (1+x) (1+x^2)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Jan 06 2018 *)
%t A018837 Array[Which[#==1,3,True,(#+Mod[#,4])/2]&,100,0] (* _Elisha Hollander_, Aug 05 2021 *)
%o A018837 (PARI) concat([0], Vec( x*(3-x+x^2-x^3-2*x^4+2*x^5)/((1-x)^2*(1+x)*(1+x^2)) + O(x^166) ) ) \\ _Joerg Arndt_, Sep 10 2014
%o A018837 (Python) def a(n): return 3 if n == 1 else (n + n % 4) // 2 # _Elisha Hollander_, Aug 05 2021
%Y A018837 Cf. A065775, A183041-A183053, A083219 (essentially the same).
%Y A018837 Cf. A018840 for the (2,3)-leaper.
%K A018837 nonn,easy
%O A018837 0,2
%A A018837 _N. J. A. Sloane_, _Marc LeBrun_