|
| |
|
|
A183041
|
|
Least number of knight's moves from (0,0) to (n,1) on infinite chessboard.
|
|
5
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
