cp's OEIS Frontend

A213476 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 7, n >= 2.

%I A213476 #9 Jun 29 2012 14:50:57
%S A213476 2,4,6,10,14,20,26,18,2,2,4,10,22,38,60,110,138,188,106,108,54,36,4,2,
%T A213476 4,10,22,50,104,194,300,444,542,840,650,1056,808,1144,354,292,16,2,4,
%U A213476 10,22,50,104,234,460,778,894,1540,1812,3444,3512,8294,6104,13914,5778,5548,2216,710,24
%N A213476 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 7, n >= 2.
%C A213476 The irregular array of numbers is:
%C A213476 ...k..3....4....5....6....7....8....9...10...11...12...13...14...15...16...17...18....19...20...21...22...23...24
%C A213476 .n
%C A213476 .2....2....4....6...10...14...20...26...18....2
%C A213476 .3....2....4...10...22...38...60..110..138..188..106..108...54...36....4
%C A213476 .4....2....4...10...22...50..104..194..300..444..542..840..650.1056..808.1144..354...292...16
%C A213476 .5....2....4...10...22...50..104..234..460..778..894.1540.1812.3444.3512.8294.6104.13914.5778.5548.2216..710...24
%C A213476 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 11, 16, 20, 24, 29, 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 for n >= k-1 is 2, 4, 10, 22, 50, 104 for which there appears to be no obvious formula.
%H A213476 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 A213476 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 A213476 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 7 node rectangle.
%Y A213476 Cf. A213106, A213249, A213431, A213433, A213473, A213474, A213475.
%K A213476 nonn,tabf
%O A213476 2,1
%A A213476 _Christopher Hunt Gribble_, Jun 12 2012