|
%I #10 Jul 23 2012 12:47:16
%S 86,0,0,0,747,119,124,109,12,0,0,0,5029,1245,1624,1537,386,106,618,
%T 898,40489,11359,15642,15239,6345,1689,6165,8214,7544,2772,12824,
%U 16728,343645,89102,125043,128224,72452,12593,39711,47539,80324,28387,113790,134553
%N Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, 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.......86......0......0......0
%C .3......747....119....124....109.....12......0......0......0
%C .4.....5029...1245...1624...1537....386....106....618....898
%C .5....40489..11359..15642..15239...6345...1689...6165...8214...7544...2772..12824..16728
%C .6...343645..89102.125043.128224..72452..12593..39711..47539..80324..28387.113790.134553
%C where k indicates the position of the end 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 is the end node (EN) of a complete non-self-adjacent simple path is
%e EN 0 1 2 3 4 5 6 7
%e 8 9 10 11 12 13 14 15
%e NT 86 0 0 0 0 0 0 86
%e 86 0 0 0 0 0 0 86
%e To limit duplication, only the top left-hand corner 86 and the three zeros to its right are stored in the sequence, i.e. T(2,1) = 86, T(2,2) = 0, T(2,3) = 0 and T(2,4) = 0.
%Y Cf. A213106, A213249, A213425, A214038, A214119, A214121, A214122, A214359, A213070, A214373.
%K nonn,tabf
%O 2,1
%A _Christopher Hunt Gribble_, Jul 14 2012
%E Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012
|
