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Least number of knight's moves from (0,0) to (n,1) on infinite chessboard.
5

%I #22 Mar 02 2021 17:20:50

%S 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,

%T 16,15,16,17,18,17,18,19,20,19,20,21,22,21,22,23,24,23,24,25,26,25,26,

%U 27,28,27,28,29,30,29,30,31,32,31,32,33,34,33,34,35,36

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

%C Row 2 of the array at A065775.

%C Apparently a(n)=A162330(n), n>0. - _R. J. Mathar_, Jan 29 2011

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

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

%F 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

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

%o (Python)

%o def a(n):

%o if n < 2: return [3, 2][n]

%o m, r = divmod(n, 4)

%o return [2*m+1, 2*m+2][r%2]

%o print([a(n) for n in range(70)]) # _Michael S. Branicky_, Mar 02 2021

%Y Cf. A065775, A018837, A183042-A183053.

%K nonn

%O 0,1

%A _Clark Kimberling_, Dec 20 2010