cp's OEIS Frontend

A214504 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 3, n >= 2.

%I A214504 #8 Jul 23 2012 12:47:02
%S A214504 12,14,32,36,36,48,80,88,86,100,188,210,209,228,204,204,418,470,472,
%T A214504 524,479,452,906,1016,1028,1152,1050,1020,1088,980,1943,2170,2219,
%U A214504 2472,2250,2222,2333,2200,4137,4610,4754,5260,4811,4738,4929,4784,4920,4924
%N A214504 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 3, n >= 2.
%C A214504 The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 2 to capture all geometrically distinct counts.
%C A214504 The quarter-rectangle is read by rows.
%C A214504 The irregular array of numbers is:
%C A214504 ....k....1....2....3....4....5....6....7....8....9...10
%C A214504 ..n
%C A214504 ..2.....12...14
%C A214504 ..3.....32...36...36...48
%C A214504 ..4.....80...88...86..100
%C A214504 ..5....188..210..209..228..204..204
%C A214504 ..6....418..470..472..524..479..452
%C A214504 ..7....906.1016.1028.1152.1050.1020.1088..980
%C A214504 ..8...1943.2170.2219.2472.2250.2222.2333.2200
%C A214504 ..9...4137.4610.4754.5260.4811.4738.4929.4784.4920.4924
%C A214504 where k indicates the position of a node in the quarter-rectangle.
%C A214504 For each n, the maximum value of k is 2*floor((n+1)/2).
%C A214504 Reading this array by rows gives the sequence.
%H A214504 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 A214504 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 A214504 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 A214504 N   0  1  2
%e A214504     3  4  5
%e A214504 NT 12 14 12
%e A214504    12 14 12
%e A214504 To limit duplication, only the top left-hand corner 12 and the 14 to its right are stored in the sequence,
%e A214504   i.e. T(2,1) = 12 and T(2,2) = 14.
%Y A214504 Cf. A213106, A213249, A213089, A213954, A214121, A214397, A214399
%K A214504 nonn,tabf
%O A214504 2,1
%A A214504 _Christopher Hunt Gribble_, Jul 19 2012
%E A214504 Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012