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%I #12 Jul 03 2012 15:55:31
%S 13,10,8,77,51,38,68,36,20,330,266,248,300,145,96,1580,1381,1365,1414,
%T 813,652,1402,596,432,7678,6630,6357,6630,3968,3192,6357,3192,2828,
%U 35971,30070,27638,30709,18037,13744,27591,14507,13851,26574,15318,17846
%N Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 6, n >= 2.
%C 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 The quarter-rectangle is read by rows.
%C The irregular array of numbers is:
%C ....k......1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12
%C ..n
%C ..2.......13....10.....8
%C ..3.......77....51....38....68....36....20
%C ..4......330...266...248...300...145....96
%C ..5.....1580..1381..1365..1414...813...652..1402...596...432
%C ..6.....7678..6630..6357..6630..3968..3192..6357..3192..2828
%C ..7....35971.30070.27638.30709.18037.13744.27591.14507.13851.26574.15318.17846
%C where k indicates the position of the start node in the quarter-rectangle.
%C For each n, the maximum value of k is 3*floor((n+1)/2).
%C Reading this array by rows gives the sequence.
%H 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 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 When n = 2, the number of times (NT) each node in the rectangle is the start node (SN) of a complete non-self-adjacent simple path is
%e SN 0 1 2 3 4 5
%e 6 7 8 9 10 11
%e NT 13 10 8 8 10 13
%e 13 10 8 8 10 13
%e To limit duplication, only the top left-hand corner 13 and the 10 and 8 to its right are stored in the sequence, i.e. T(2,1) = 13, T(2,2) = 10 and T(2,3) = 8.
%Y Cf. A213106, A213249, A213375, A213478, A213954, A214022, A214023
%K nonn,tabf
%O 2,1
%A _Christopher Hunt Gribble_, Jul 01 2012