A018838 Minimum number of steps for a knight to reach (n,n) on an infinite chessboard.

0, 2, 4, 2, 4, 4, 4, 6, 6, 6, 8, 8, 8, 10, 10, 10, 12, 12, 12, 14, 14, 14, 16, 16, 16, 18, 18, 18, 20, 20, 20, 22, 22, 22, 24, 24, 24, 26, 26, 26, 28, 28, 28, 30, 30, 30, 32, 32, 32, 34, 34, 34, 36, 36, 36, 38, 38, 38, 40, 40, 40, 42, 42, 42, 44, 44, 44

Offset

0,2

Comments

Apparently also the minimum number of steps of the (1,3)-leaper to reach (2n,0) starting at (0,0). The (1,3)-leaper cannot reach (2n+1,0). - R. J. Mathar, Jan 05 2018

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Formula

a(n) = 2*ceiling(n/3) = 2*A002264(n+2), n >= 3.

G.f.: 2*x*(x^5-x^4-x^2+x+1)/((x-1)^2*(x^2+x+1)). - Colin Barker, Oct 04 2012

Mathematica

Join[{0, 2, 4}, Table[2*Ceiling[n/3], {n, 3, 70}]] (* Harvey P. Dale, Jul 27 2012 *)
CoefficientList[Series[2 x (x^5 - x^4 - x^2 + x + 1)/((x - 1)^2 (x^2 + x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Oct 16 2013 *)
LinearRecurrence[{1, 0, 1, -1}, {0, 2, 4, 2, 4, 4, 4}, 70] (* Harvey P. Dale, Nov 03 2019 *)

Prog

(Magma) [0, 2, 4] cat [2*Ceiling(n/3): n in [3..80]]; // Vincenzo Librandi, Oct 16 2013
(PARI) a(n)=if(n>2, (n+2)\3*2, 2*n) \\ Charles R Greathouse IV, Feb 10 2017

Crossrefs

Sequence in context: A143235 A069465 A047947 * A116982 A216621 A300448

Adjacent sequences: A018835 A018836 A018837 * A018839 A018840 A018841

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Marc LeBrun

Status

approved