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A363894
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Number of weakly connected components of a halved addsub configuration graph with respect to integers mod n over a path with two vertices.
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0
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1, 2, 1, 8, 2, 3, 1, 5, 8, 4, 2, 18, 3, 33, 1, 19, 5, 6, 8, 20, 4, 7, 2, 39, 18, 14, 3, 32, 33, 25, 1, 29, 19, 58, 5, 42, 6, 75, 8, 91, 20, 34, 4, 108, 7, 13, 2, 17, 39, 164, 18, 58, 14, 83, 3, 47, 32, 16, 33, 66, 25, 167, 1, 365, 29, 18, 19, 56, 58, 19, 5
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OFFSET
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2,2
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COMMENTS
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The addsub game is played on a path with two vertices {u,v}. We define a configuration of the integers mod n on {u,v} by assigning weights wt(u) and wt(v).
An addsub move from u to v is a reassignment of weights given by wt(u) -> wt(u) - wt(v) (mod n) and wt(v) -> wt(u) + wt(v) (mod n). An addsub move from v to u (i.e. the backward move) is defined analogously.
The halved addsub configuration graph is the directed subgraph of the addsub configuration graph restricted to the forward move only: wt(u) -> wt(u) - wt(v) (mod n) and wt(v) -> wt(u) + wt(v) (mod n).
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REFERENCES
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E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 1, CRC Press, 2001.
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LINKS
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MATHEMATICA
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Upto=25;
Table[
VertexSet:={};
EdgeSet:={};
(* Compute configuration graph for integers mod n *)
Do[
Do[AppendTo[VertexSet, {i, j}];
AppendTo[EdgeSet, {i, j}\[DirectedEdge]{Mod[i-j, n], Mod[i+j, n]}],
{j, 0, n-1}],
{i, 0, n-1}];
(* Print n-th term *)
Length[WeaklyConnectedComponents[Graph[VertexSet, EdgeSet]]],
{n, 2, Upto}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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