A051261 -id:A051261 - cp's OEIS frontend

A077226 Inverse of A051261, i.e., (n, a(n), a(n)) is a winning position in 3-pile Wythoff game.

0, 3, 7, 4, 1, 8, 2, 5, 17, 13, 9, 6, 19, 21, 29, 27, 32, 10, 28, 25, 33, 12, 56, 11, 16, 36, 15, 41, 14, 23, 59, 51, 22, 61, 18, 20, 73, 69, 84, 58, 57, 62, 65, 81, 24, 26, 64, 89, 35, 100, 75, 78, 76, 109, 37, 116, 31, 30, 34, 111, 126, 92, 44, 98, 86, 124, 45, 121, 94, 99

Offset: 0

Christian G. Bower, Oct 29 2002

nonn

Index entries for sequences that are permutations of the natural numbers

Cf. A018219.

A018219 Table T(a,b) by antidiagonals of winning positions in 3-pile Wythoff game (a square array).

Original entry on oeis.org

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

Offset: 0

Michael Kleber

(a,b,T(a,b)) are the winning positions in 3-pile Wythoff game. A move in k-pile 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.

			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.

Rows 0-3: A002251, A018220-A018222. Main diagonal: A051261.

T(a, b)=0 iff A004481(a, b)=0 iff A002251(a)=b.

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[ a-i, b ], {i, a} ] ], f[ Table[ T[ a, b-i ], {i, b} ] ], f[ Table[ T[ a-i, b-i ], {i, Min[ a, b ]} ] ] } ]

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

cp's OEIS Frontend

A077226 Inverse of A051261, i.e., (n, a(n), a(n)) is a winning position in 3-pile Wythoff game.

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A018219 Table T(a,b) by antidiagonals of winning positions in 3-pile Wythoff game (a square array).

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