%I #9 Jul 03 2012 15:55:42
%S 8,7,6,36,25,20,32,18,12,122,102,94,110,52,32,436,395,394,395,220,154,
%T 394,154,80,1580,1414,1402,1381,813,596,1365,652,432,5600,4829,4650,
%U 4795,2792,2036,4453,2285,1712,4412,2556,2248,19287,16131,15246,16735,9444,6758,15113,7697,5858,13878,8612,8496
%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 5, 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........8.....7.....6
%C ..3.......36....25....20....32....18....12
%C ..4......122...102....94...110....52....32
%C ..5......436...395...394...395...220...154...394...154....80
%C ..6.....1580..1414..1402..1381...813...596..1365...652...432
%C ..7.....5600..4829..4650..4795..2792..2036..4453..2285..1712..4412..2556..2248
%C ..8....19287.16131.15246.16735..9444..6758.15113..7697..5858.13878..8612..8496
%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
%e 5 6 7 8 9
%e NT 8 7 6 7 8
%e 8 7 6 7 8
%e To limit duplication, only the top left-hand corner 8 and the 7 and 6 to its right are stored in the sequence, i.e. T(2,1) = 8, T(2,2) = 7 and T(2,3) = 6.
%Y Cf. A213106, A213249, A213375, A213478, A213954, A214022
%K nonn,tabf
%O 2,1
%A _Christopher Hunt Gribble_, Jul 01 2012
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