cp's OEIS Frontend

A214503 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.

%I A214503 #13 Jul 23 2012 12:48:27
%S A214503 113,116,116,122,906,1028,1050,1088,1016,1152,1020,980,6751,8562,9411,
%T A214503 9718,8651,8317,7116,6882,50036,69029,80263,82942,71736,67670,61229,
%U A214503 60116,81276,63148,46550,44196,335569,482769,577787,600124,494659,488710,465142,458850,599448,463257,353704,341918
%N A214503 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 A214503 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 A214503 The quarter-rectangle is read by rows.
%C A214503 The irregular array of numbers is:
%C A214503 ...k......1......2......3......4......5......6......7......8......9.....10.....11.....12
%C A214503 .n
%C A214503 .2......113....116....116....122
%C A214503 .3......906...1028...1050...1088...1016...1152...1020....980
%C A214503 .4.....6751...8562...9411...9718...8651...8317...7116...6882
%C A214503 .5....50036..69029..80263..82942..71736..67670..61229..60116..81276..63148..46550..44196
%C A214503 .6...335569.482769.577787.600124.494659.488710.465142.458850.599448.463257.353704.341918
%C A214503 where k indicates the position of a node in the quarter-rectangle.
%C A214503 For each n, the maximum value of k is 4*floor((n+1)/2).
%C A214503 Reading this array by rows gives the sequence.
%H A214503 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 A214503 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 A214503 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 A214503 N    0   1   2   3   4   5   6
%e A214503      7   8   9  10  11  12  13
%e A214503 NT 113 116 116 122 116 116 113
%e A214503    113 116 116 122 116 116 113
%e A214503 To limit duplication, only the top left-hand corner 113 and the 116, 116, 122 to its right are stored in the sequence,
%e A214503 i.e. T(2,1) = 113, T(2,2) = 116, T(2,3) = 116 and T(2,4) = 122.
%Y A214503 Cf. A213106, A213249, A213383, A214037, A214373, A214397, A214399, A214504, A214510, A214563, A214601
%K A214503 nonn,tabf
%O A214503 2,1
%A A214503 _Christopher Hunt Gribble_, Jul 22 2012