cp's OEIS Frontend

A214025 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.

%I A214025 #12 Jul 03 2012 15:55:31
%S A214025 13,10,8,77,51,38,68,36,20,330,266,248,300,145,96,1580,1381,1365,1414,
%T A214025 813,652,1402,596,432,7678,6630,6357,6630,3968,3192,6357,3192,2828,
%U A214025 35971,30070,27638,30709,18037,13744,27591,14507,13851,26574,15318,17846
%N A214025 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 A214025 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 A214025 The quarter-rectangle is read by rows.
%C A214025 The irregular array of numbers is:
%C A214025 ....k......1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12
%C A214025 ..n
%C A214025 ..2.......13....10.....8
%C A214025 ..3.......77....51....38....68....36....20
%C A214025 ..4......330...266...248...300...145....96
%C A214025 ..5.....1580..1381..1365..1414...813...652..1402...596...432
%C A214025 ..6.....7678..6630..6357..6630..3968..3192..6357..3192..2828
%C A214025 ..7....35971.30070.27638.30709.18037.13744.27591.14507.13851.26574.15318.17846
%C A214025 where k indicates the position of the start node in the quarter-rectangle.
%C A214025 For each n, the maximum value of k is 3*floor((n+1)/2).
%C A214025 Reading this array by rows gives the sequence.
%H A214025 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 A214025 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 A214025 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 A214025 SN  0  1  2  3  4  5
%e A214025     6  7  8  9 10 11
%e A214025 NT 13 10  8  8 10 13
%e A214025    13 10  8  8 10 13
%e A214025 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 A214025 Cf. A213106, A213249, A213375, A213478, A213954, A214022, A214023
%K A214025 nonn,tabf
%O A214025 2,1
%A A214025 _Christopher Hunt Gribble_, Jul 01 2012