

A140518


Number of simple paths from corner to corner of an n X n grid with kingmoves allowed.


6



1, 5, 235, 96371, 447544629, 22132498074021, 10621309947362277575, 50819542770311581606906543, 2460791237088492025876789478191411, 1207644919895971862319430895789323709778193, 5996262208084349429209429097224046573095272337986011
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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, zerosuppressed binary decision diagram").


REFERENCES

Donald E. Knuth, The Art of Computer Programming, Vol. 4, fascicle 1, section 7.1.4, p. 117, AddisonWesley, 2009.


LINKS

Table of n, a(n) for n=1..11.


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

Main diagonal of A329118.
Cf. A140519, A158651, A234622, A007764, A038496.
Cf. A220638 (Hosoya index).
Sequence in context: A265957 A137085 A153025 * A269551 A200962 A270052
Adjacent sequences: A140515 A140516 A140517 * A140519 A140520 A140521


KEYWORD

nonn,walk


AUTHOR

Don Knuth, Jul 26 2008


EXTENSIONS

a(9)a(11) from Andrew Howroyd, Apr 07 2016


STATUS

approved



