cp's OEIS Frontend

A213070 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 6, n >= 2.

%I A213070 #25 Jul 23 2012 12:46:36
%S A213070 31,0,0,165,27,32,8,0,0,720,187,236,104,30,108,3431,992,1179,746,251,
%T A213070 580,920,352,1210,16608,4361,5027,4361,1094,2043,5027,2043,6268,76933,
%U A213070 17601,20009,21068,3675,7213,26181,9258,26414,25090,10048,32132
%N A213070 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 6, n >= 2.
%C A213070 The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 3 to capture all geometrically distinct counts.
%C A213070 The quarter-rectangle is read by rows.
%C A213070 The irregular array of numbers is:
%C A213070 ...k.....1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12
%C A213070 .n
%C A213070 .2......31.....0.....0
%C A213070 .3.....165....27....32.....8.....0.....0
%C A213070 .4.....720...187...236...104....30...108
%C A213070 .5....3431...992..1179...746...251...580...920...352..1210
%C A213070 .6...16608..4361..5027..4361..1094..2043..5027..2043..6268
%C A213070 .7...76933.17601.20009.21068..3675..7213.26181..9258.26414.25090.10048.32132
%C A213070 where k indicates the position of the end node in the quarter-rectangle.
%C A213070 For each n, the maximum value of k is 3*floor((n+1)/2).
%C A213070 Reading this array by rows gives the sequence.
%H A213070 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 A213070 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 A213070 When n = 2, the number of times (NT) each node in the rectangle is the end node (EN) of a complete non-self-adjacent simple path is
%e A213070 EN  0  1  2  3  4  5
%e A213070     6  7  8  9 10 11
%e A213070 NT 31  0  0  0  0 31
%e A213070    31  0  0  0  0 31
%e A213070 To limit duplication, only the top left-hand corner 31 and the two zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0 and T(2,3) = 0.
%Y A213070 Cf. A213106, A213249, A213379, A214025, A214119, A214121, A214122, A214359.
%K A213070 nonn,tabf
%O A213070 2,1
%A A213070 _Christopher Hunt Gribble_, Jul 13 2012
%E A213070 Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012