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A018837
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Number of steps for knight to reach (n,0) on infinite chess-board.
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4
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0, 3, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 16, 17, 16, 17, 18, 19, 18, 19, 20, 21, 20, 21, 22, 23, 22, 23, 24, 25, 24, 25, 26, 27, 26, 27
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The knight starts at (0,0) and we count the least number of steps. Row 1 of the array at A065775. - Clark Kimberling, Dec 20 2010
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FORMULA
| 2[ (n+2)/4 ] if n even, 2[ (n+1)/4 ]+1 if n odd (n >= 8).
G.f.: x(3-x+x^2-x^3-2x^4+2x^5)/((1-x)^2*(1+x)(1+x^2)). a(n)=A083219(n), n<>1. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 15 2008]
T(0,0)=0, T(1,0)=3, and for m>=1, T(4m-2,0)=2m, T(4m-1,0)=2m+1, T(4m,0)=2m,
T(4m+1,0)=2m+1 where T(.,.) = A065775(.,.). - Clark Kimberling, Dec 20 2010
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EXAMPLE
| a(1)=3 counts these moves: (0,0) to (2,1) to (0,2) to (1,0) - Clark Kimberling, Dec 20 2010
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CROSSREFS
| Cf. A065775, A183041-A183053. - Clark Kimberling, Dec 20 2010
Sequence in context: A168330 A176059 A029211 * A097618 A039639 A023509
Adjacent sequences: A018834 A018835 A018836 * A018838 A018839 A018840
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Marc LeBrun (mlb(AT)well.com)
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