cp's OEIS Frontend

A214359 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 5, n >= 2.

%I A214359 #13 Jul 23 2012 12:46:10
%S A214359 18,0,0,75,13,16,6,0,0,256,67,88,52,14,32,932,246,308,246,80,130,308,
%T A214359 130,288,3431,746,920,992,251,352,1179,580,1210,12027,2143,2612,3522,
%U A214359 640,954,4399,1941,3956,4170,2394,5136,40489,6345,7544,11359,1689,2772,15642,6165,12824,15239,8214,16728
%N A214359 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 5, n >= 2.
%C A214359 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 A214359 The quarter-rectangle is read by rows.
%C A214359 The irregular array of numbers is:
%C A214359 ...k.....1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12
%C A214359 .n
%C A214359 .2......18.....0.....0
%C A214359 .3......75....13....16.....6.....0.....0
%C A214359 .4.....256....67....88....52....14....32
%C A214359 .5.....932...246...308...246....80...130...308...130...288
%C A214359 .6....3431...746...920...992...251...352..1179...580..1210
%C A214359 .7...12027..2143..2612..3522...640...954..4399..1941..3956..4170..2394..5136
%C A214359 .8...40489..6345..7544.11359..1689..2772.15642..6165.12824.15239..8214.16728
%C A214359 where k indicates the position of the end node in the quarter-rectangle.
%C A214359 For each n, the maximum value of k is 3*floor((n+1)/2).
%C A214359 Reading this array by rows gives the sequence.
%H A214359 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 A214359 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 A214359 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 A214359 EN  0  1  2  3  4
%e A214359     5  6  7  8  9
%e A214359 NT 18  0  0  0 18
%e A214359    18  0  0  0 18
%e A214359 To limit duplication, only the top left-hand corner 18 and the two zeros to its right are stored in the sequence, i.e. T(2,1) = 10, T(2,2) = 0 and T(2,3) = 0.
%Y A214359 Cf. A213106, A213249, A213375, A214023, A214119, A214121, A214122.
%K A214359 nonn,tabf
%O A214359 2,1
%A A214359 _Christopher Hunt Gribble_, Jul 13 2012
%E A214359 Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012