|
%I #10 Jun 22 2012 13:16:15
%S 4,4,6,10,14,20,30,44,60,60,28,2,4,8,16,22,54,70,152,238,416,574,810,
%T 642,760,456,320,136,72,8,4,8,20,40,84,126,268,418,1014,1450,2890,
%U 3510,5474,5286,7238,6926,8218,5636,6754,2956,4220,778,48
%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 9, 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...25
%C .n
%C .2....4....4....6...10...14...20...30...44...60...60...28....2
%C .3....4....8...16...22...54...70..152..238..416..574..810..642..760..456..320..136...72....8
%C .4....4....8...20...40...84..126..268..418.1014.1450.2890.3510.5474.5286.7238.6926.8218.5636.6754.2956.4220..778...48
%C where k is the path length in nodes. There is insufficient evidence to attempt to define the irregularity of the array. However, the maximum values of k for 2 <= n <= 10 are 14, 20, 25, 30, 36, 42, 48, 53. 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 9 node rectangle.
%Y Cf. A213106, A213249, A213274, A213089, A213342, A213375, A213379, A213383, A213425.
%K nonn,tabf
%O 2,1
%A _Christopher Hunt Gribble_, Jun 11 2012
|
