cp's OEIS Frontend

A213379 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 6, n >= 2.

%I A213379 #12 Jun 22 2012 13:13:08
%S A213379 4,4,6,10,14,16,8,4,8,16,22,48,60,82,90,66,34,24,2,4,8,20,40,78,116,
%T A213379 192,180,354,278,530,268,546,124,32,4,8,20,44,106,172,322,410,612,602,
%U A213379 1462,1122,3240,1712,4682,1394,706,218,4
%N A213379 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 6, n >= 2.
%C A213379 The irregular array of numbers is:
%C A213379 ...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20...21
%C A213379 .n
%C A213379 .2....4....4....6...10...14...16....8
%C A213379 .3....4....8...16...22...48...60...82...90...66...34...24....2
%C A213379 .4....4....8...20...40...78..116..192..180..354..278..530..268..546..124...32
%C A213379 .5....4....8...20...44..106..172..322..410..612..602.1462.1122.3240.1712.4682.1394..706..218....4
%C A213379 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 4n - floor((n-8)/4) for n >= 8. 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 A213379 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 A213379 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 A213379 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 6 node rectangle.
%Y A213379 Cf. A213106, A213249, A213274, A213089, A213342, A213375.
%K A213379 nonn,tabf
%O A213379 2,1
%A A213379 _Christopher Hunt Gribble_, Jun 10 2012