A214503 - OEIS

%I #13 Jul 23 2012 12:48:27

%S 113,116,116,122,906,1028,1050,1088,1016,1152,1020,980,6751,8562,9411,

%T 9718,8651,8317,7116,6882,50036,69029,80263,82942,71736,67670,61229,

%U 60116,81276,63148,46550,44196,335569,482769,577787,600124,494659,488710,465142,458850,599448,463257,353704,341918

%N Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths incorporating each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 7, 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 4 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......113....116....116....122

%C .3......906...1028...1050...1088...1016...1152...1020....980

%C .4.....6751...8562...9411...9718...8651...8317...7116...6882

%C .5....50036..69029..80263..82942..71736..67670..61229..60116..81276..63148..46550..44196

%C .6...335569.482769.577787.600124.494659.488710.465142.458850.599448.463257.353704.341918

%C where k indicates the position of a node in the quarter-rectangle.

%C For each n, the maximum value of k is 4*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 (N) occurs in a complete non-self-adjacent simple path is

%e N    0   1   2   3   4   5   6

%e      7   8   9  10  11  12  13

%e NT 113 116 116 122 116 116 113

%e    113 116 116 122 116 116 113

%e To limit duplication, only the top left-hand corner 113 and the 116, 116, 122 to its right are stored in the sequence,

%e i.e. T(2,1) = 113, T(2,2) = 116, T(2,3) = 116 and T(2,4) = 122.

%Y Cf. A213106, A213249, A213383, A214037, A214373, A214397, A214399, A214504, A214510, A214563, A214601

%K nonn,tabf

%O 2,1

%A _Christopher Hunt Gribble_, Jul 22 2012