|
|
A140518
|
|
Number of simple paths from corner to corner of an n X n grid with king-moves allowed.
|
|
9
|
|
|
1, 5, 235, 96371, 447544629, 22132498074021, 10621309947362277575, 50819542770311581606906543, 2460791237088492025876789478191411, 1207644919895971862319430895789323709778193, 5996262208084349429209429097224046573095272337986011
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
This graph is the "strong product" of P_n with P_n, where P_n is a path of length n. Sequence A007764 is what we get when we restrict ourselves to rook moves of unit length.
Computed using ZDDs (ZDD = "reduced, order, zero-suppressed binary decision diagram").
|
|
REFERENCES
|
Donald E. Knuth, The Art of Computer Programming, Vol. 4, fascicle 1, section 7.1.4, p. 117, Addison-Wesley, 2009.
|
|
LINKS
|
|
|
EXAMPLE
|
For example, when n=8 this is the number of ways to move a king from a1 to h8 without occupying any cell twice.
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,walk
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|