cp's OEIS Frontend

A214373 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 7, n >= 2.

%I A214373 #10 Jul 23 2012 12:46:23
%S A214373 52,0,0,0,353,57,62,60,10,0,0,0,1931,495,622,602,200,56,262,364,12027,
%T A214373 3522,4399,4170,2143,640,1941,2394,2612,954,3956,5136,76933,21068,
%U A214373 26181,25090,17601,3675,9258,10048,20009,7213,26414,32132
%N A214373 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 7, n >= 2.
%C A214373 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 A214373 The quarter-rectangle is read by rows.
%C A214373 The irregular array of numbers is:
%C A214373 ...k.....1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12
%C A214373 .n
%C A214373 .2......52.....0.....0.....0
%C A214373 .3.....353....57....62....60....10.....0.....0.....0
%C A214373 .4....1931...495...622...602...200....56...262...364
%C A214373 .5...12027..3522..4399..4170..2143...640..1941..2394..2612...954..3956..5136
%C A214373 .6...76933.21068.26181.25090.17601..3675..9258.10048.20009..7213.26414.32132
%C A214373 where k indicates the position of the end node in the quarter-rectangle.
%C A214373 For each n, the maximum value of k is 4*floor((n+1)/2).
%C A214373 Reading this array by rows gives the sequence.
%H A214373 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 A214373 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 A214373 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 A214373 EN  0  1  2  3  4  5  6
%e A214373     7  8  9 10 11 12 13
%e A214373 NT 52  0  0  0  0  0 52
%e A214373    52  0  0  0  0  0 52
%e A214373 To limit duplication, only the top left-hand corner 52 and the three zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0, T(2,3) = 0 and T(2,4) = 0.
%Y A214373 Cf. A213106, A213249, A213383, A214037, A214119, A214121, A214122, A214359, A213070.
%K A214373 nonn,tabf
%O A214373 2,1
%A A214373 _Christopher Hunt Gribble_, Jul 14 2012
%E A214373 Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012