

A018219


Table T(a,b) by antidiagonals of winning positions in 3pile Wythoff game (a square array).


7



0, 2, 2, 1, 4, 1, 5, 0, 0, 5, 7, 3, 6, 3, 7, 3, 1, 8, 8, 1, 3, 10, 6, 10, 1, 10, 6, 10, 4, 5, 12, 4, 4, 12, 5, 4, 13, 12, 2, 0, 3, 0, 2, 12, 13, 15, 15, 7, 9, 11, 11, 9, 7, 15, 15, 6, 17, 3, 11, 15, 7, 15, 11, 3, 17, 6, 18, 14, 11, 2, 0, 1, 1, 0, 2, 11, 14, 18, 20, 20, 4, 6, 19, 5, 11, 5, 19, 6
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OFFSET

0,2


COMMENTS

(a,b,T(a,b)) are the winning positions in 3pile Wythoff game. A move in kpile Wythoff is: pick a subset of the k piles and remove the same number of stones from each. Goal: take the last stone.
T(a,b) = T(b,a). If T(a,b)=c then T(a,c)=b and T(b,c)=a.


LINKS

Table of n, a(n) for n=0..87.


EXAMPLE

0 2 1 5 7 ...
2 4 0 3 1 ...
1 0 6 8 10 ...
5 3 8 1 4 ...
7 1 10 4 3 ...
T(1,1)=4, since from (114) your opponent can move to (113),(112),(111),(110),(014),(013),(004),(003). You can either win or move to (012) and win a move later.


MATHEMATICA

mex[ s_ ] := Min[ Complement[ Range[ 0, Max[ {s, 1} ]+1 ], Flatten[ s ] ] ]; f[ s_ ] := Join[ s, s+Table[ i, {i, Length[ s ]} ] ]; T[ a_, b_ ] := T[ a, b ] = mex[ { f[ Table[ T[ ai, b ], {i, a} ] ], f[ Table[ T[ a, bi ], {i, b} ] ], f[ Table[ T[ ai, bi ], {i, Min[ a, b ]} ] ] } ]


CROSSREFS

Rows 03: A002251, A018220A018222. Main diagonal: A051261.
T(a, b)=0 iff A004481(a, b)=0 iff A002251(a)=b.
Sequence in context: A268193 A238606 A054995 * A174714 A116633 A263232
Adjacent sequences: A018216 A018217 A018218 * A018220 A018221 A018222


KEYWORD

nonn,tabl


AUTHOR

Michael Kleber


EXTENSIONS

Edited and extended by Christian G. Bower, Oct 29 2002


STATUS

approved



