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

Author

Clark Kimberling, Dec 20 2010

Keywords

• nonn

Comments

Row 2 of the array at A065775.

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

Examples

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

Crossrefs

Cf. A065775, A018837, A183042-A183053.

Programs

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

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