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%I #18 Mar 31 2023 15:31:27
%S 1,5,235,96371,447544629,22132498074021,10621309947362277575,
%T 50819542770311581606906543,2460791237088492025876789478191411,
%U 1207644919895971862319430895789323709778193,5996262208084349429209429097224046573095272337986011
%N Number of simple paths from corner to corner of an n X n grid with king-moves allowed.
%C 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.
%C Computed using ZDDs (ZDD = "reduced, order, zero-suppressed binary decision diagram").
%D Donald E. Knuth, The Art of Computer Programming, Vol. 4, fascicle 1, section 7.1.4, p. 117, Addison-Wesley, 2009.
%H Jens Weise, <a href="https://opendata.uni-halle.de/bitstream/1981185920/103345/1/Weise_Jens_Dissertation_2023.pdf">Evolutionary Many-Objective Optimisation for Pathfinding Problems</a>, Ph. D. Dissertation, Otto von Guercke Univ., Magdeburg (Germany, 2022), see p. 53.
%e For example, when n=8 this is the number of ways to move a king from a1 to h8 without occupying any cell twice.
%Y Main diagonal of A329118.
%Y Cf. A140519, A158651, A234622, A007764, A038496.
%Y Cf. A220638 (Hosoya index).
%K nonn,walk
%O 1,2
%A _Don Knuth_, Jul 26 2008
%E a(9)-a(11) from _Andrew Howroyd_, Apr 07 2016
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