cp's OEIS Frontend

A213473 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 4, n >= 2.

%I A213473 #10 Jun 29 2012 11:24:02
%S A213473 2,4,6,6,2,4,10,18,8,8,14,2,4,10,18,20,12,18,8,42,2,4,10,22,46,66,60,
%T A213473 56,106,72,236,26,2,4,10,22,50,100,152,158,230,246,410,260,546,124,32,
%U A213473 2,4,10,22,50,104,194,300,444,542,840,650,1056,808,1144,354,292,16
%N A213473 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 4, n >= 2.
%C A213473 The irregular array of numbers is:
%C A213473 ...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18...19...20
%C A213473 .n
%C A213473 .2....2....4....6....6
%C A213473 .3....2....4...10...18....8....8...14
%C A213473 .4....2....4...10...18...20...12...18....8...42
%C A213473 .5....2....4...10...22...46...66...60...56..106...72..236...26
%C A213473 .6....2....4...10...22...50..100..152..158..230..246..410..260..546..124...32
%C A213473 .7....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354..292...16
%C A213473 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 <= 12 are 6, 9, 11, 14, 17, 20, 22, 25, 28, 30, 33. 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, where n >= k-1, is 2, 4, 10, 22, 50, 104, 198, 354, 710, 1288, 2600 for which there appears to be no obvious formula.
%H A213473 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 A213473 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 A213473 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 4 node rectangle.
%Y A213473 Cf. A213106, A213249, A213431, A213433.
%K A213473 nonn,tabf
%O A213473 2,1
%A A213473 _Christopher Hunt Gribble_, Jun 12 2012