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%I #15 Jun 20 2012 13:42:47
%S 4,4,6,10,10,2,4,8,16,22,42,24,42,22,18,4,8,20,40,72,80,90,66,184,72,
%T 236,26,4,8,20,44,100,136,220,156,348,244,800,336,1308,248,56,4,8,20,
%U 44,106,172,322,410,612,602,1462,1122,3240,1712,4682,1394,706,218,4
%N Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 5, n >= 2.
%C The irregular array of numbers is:
%C ...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16....17...18....19...20...21...22...23...24
%C .n
%C .2....4....4....6...10...10....2
%C .3....4....8...16...22...42...24...42...22...18
%C .4....4....8...20...40...72...80...90...66..184...72..236...26
%C .5....4....8...20...44..100..136..220..156..348..244..800..336.1308..248....56
%C .6....4....8...20...44..106..172..322..410..612..602.1462.1122.3240.1712..4682.1394...706..218...4
%C where k is the path length in nodes. In an attempt to define the irregularity of the array, it appears that the maximum value of k is 3n+2 for 2 <= n <= 5, 3n+3 for 6 <= n <= 9 and 3n+4 for n >= 10. Reading this array by rows gives the sequence. One half of the numbers of paths constitute the sequence to remove the effect of the bilateral symmetry of the rectangle.
%H 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 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 T(2,3) = One half of the number of complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 5 node rectangle.
%Y Cf. A213106, A213249, A213274, A213089, A213342.
%K nonn,tabf
%O 2,1
%A _Christopher Hunt Gribble_, Jun 10 2012
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