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A140518 Number of simple paths from corner to corner of an n X n grid with king-moves allowed. 4
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

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

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

AUTHOR

Don Knuth, Jul 26 2008

EXTENSIONS

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

STATUS

approved

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Last modified April 22 14:52 EDT 2019. Contains 322356 sequences. (Running on oeis4.)