A183041 Least number of knight's moves from (0,0) to (n,1) on infinite chessboard.

3, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 8, 7, 8, 9, 10, 9, 10, 11, 12, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 17, 18, 17, 18, 19, 20, 19, 20, 21, 22, 21, 22, 23, 24, 23, 24, 25, 26, 25, 26, 27, 28, 27, 28, 29, 30, 29, 30, 31, 32, 31, 32, 33, 34, 33, 34, 35, 36

Offset

0,1

Comments

Row 2 of the array at A065775.

Apparently a(n)=A162330(n), n>0. - R. J. Mathar, Jan 29 2011

Links

Table of n, a(n) for n=0..69.

Formula

T(0,1)=3, T(1,1)=2, and for m>=1,

T(4m-2,1)=2m-1, T(4m-1,1)=2m, T(4m,1)=2m+1, T(4m+1,1)=2m+2.

G.f.: (2*x^5-2*x^4+x^3-x^2-x+3) / ((x-1)^2*(x+1)*(x^2+1)). - Colin Barker, Feb 19 2014

Example

a(0)=3 counts (0,0) to (2,1) to (1,3) to (0,1).

Prog

(Python)
def a(n):
  if n < 2: return [3, 2][n]
  m, r = divmod(n, 4)
  return [2*m+1, 2*m+2][r%2]
print([a(n) for n in range(70)]) # Michael S. Branicky, Mar 02 2021

Crossrefs

Cf. A065775, A018837, A183042-A183053.

Sequence in context: A256427 A120441 A232191 * A136560 A105847 A240485

Adjacent sequences: A183038 A183039 A183040 * A183042 A183043 A183044

Keyword

nonn

Author

Clark Kimberling, Dec 20 2010

Status

approved