cp's OEIS Frontend

A213475 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the 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 A213475 #9 Jun 29 2012 14:13:23
%S A213475 2,4,6,10,14,16,8,2,4,10,22,38,56,68,80,58,34,24,2,2,4,10,22,50,100,
%T A213475 152,158,230,246,410,260,546,124,32,2,4,10,22,50,100,192,318,340,430,
%U A213475 726,816,1786,1454,4626,1394,706,218,4
%N A213475 Irregular array T(n,k) of the numbers of distinct shapes under rotation of the 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 A213475 The irregular array of numbers is:
%C A213475 ...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20...21
%C A213475 .n
%C A213475 .2....2....4....6...10...14...16....8
%C A213475 .3....2....4...10...22...38...56...68...80...58...34...24....2
%C A213475 .4....2....4...10...22...50..100..152..158..230..246..410..260..546..124...32
%C A213475 .5....2....4...10...22...50..100..192..318..340..430..726..816.1786.1454.4626.1394..706..218....4
%C A213475 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 <= 7 are 9, 14, 17, 21, 24, 29. Reading this array by rows gives the sequence. The asymptotic sequence for the number of distinct shapes under rotation of the complete non-self-adjacent simple paths of each nodal length k for n >= k-1 is 2, 4, 10, 22, 50, 104 for which there appears to be no obvious formula.
%H A213475 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 A213475 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 A213475 T(2,3) = The number of distinct shapes under rotation of the complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 6 node rectangle.
%Y A213475 Cf. A213106, A213249, A213431, A213433, A213473, A213474.
%K A213475 nonn,tabf
%O A213475 2,1
%A A213475 _Christopher Hunt Gribble_, Jun 12 2012