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A214397 Triangle T(n,k) of the numbers of nodes in all non-extendable (complete) non-self-adjacent simple paths within a square lattice bounded by rectangles with nodal dimensions n and k, n >= k >= 2.

%I A214397 #5 Jul 18 2012 21:07:08
%S A214397 24,76,320,188,1040,4608,408,2756,18636,104272,832,8368,67952,513460,
%T A214397 3349208,1624,21468,228432,2312112,19845964,152434216,3080,53108,
%U A214397 730772,9943160,113061272,1125079096,10676325280,5716,128072,2261792,41508164,629214072,8150708696,99701732480,1200653865056
%N A214397 Triangle T(n,k) of the numbers of nodes in all non-extendable (complete) non-self-adjacent simple paths within a square lattice bounded by rectangles with nodal dimensions n and k, n >= k >= 2.
%C A214397 The triangle of numbers is:
%C A214397 ....k.....2......3.......4........5.........6..........7...........8.............9
%C A214397 .n
%C A214397 .2.......24
%C A214397 .3.......76....320
%C A214397 .4......188...1040....4608
%C A214397 .5......408...2756...18636...104272
%C A214397 .6......832...8368...67952...513460...3349208
%C A214397 .7.....1624..21468..228432..2312112..19845964..152434216
%C A214397 .8.....3080..53108..730772..9943160.113061272.1125079096.10676325280
%C A214397 .9.....5716.128072.2261792.41508164.629214072.8150708696.99701732480.1200653865056
%C A214397 Reading this triangle by rows gives the sequence.
%H A214397 C. H. Gribble, <a href="https://oeis.org/wiki/Complete_non-self-adjacent_paths:Results_for_Square_Lattice">Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.</a>
%H A214397 C. H. Gribble, <a href="https://oeis.org/wiki/Complete non-self-adjacent paths:Program">Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.</a>
%e A214397 T(2,2) = The number of nodes in all complete non-self-adjacent simple paths within a 2 X 2 node rectangle.
%Y A214397 Cf. A213106, A213249.
%K A214397 nonn,tabl
%O A214397 2,1
%A A214397 _Christopher Hunt Gribble_, Jul 15 2012