cp's OEIS Frontend

A214510 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 4, n >= 2.

%I A214510 #8 Jul 23 2012 12:47:29
%S A214510 23,24,80,86,88,100,264,303,303,282,820,1008,1007,907,1058,776,2401,
%T A214510 3043,3013,2844,3312,2375,6751,8651,8562,8317,9411,7116,9718,6882,
%U A214510 18630,24035,23979,23261,26077,20216,26479,20016,50775,65977,66474,63790,72137,55400,71469,55907,69764,57274
%N A214510 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 4, n >= 2.
%C A214510 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 A214510 The quarter-rectangle is read by rows.
%C A214510 The irregular array of numbers is:
%C A214510 ...k.....1.....2.....3.....4.....5.....6.....7.....8.....9....10
%C A214510 .n
%C A214510 .2......23....24
%C A214510 .3......80....86....88...100
%C A214510 .4.....264...303...303...282
%C A214510 .5.....820..1008..1007...907..1058...776
%C A214510 .6....2401..3043..3013..2844..3312..2375
%C A214510 .7....6751..8651..8562..8317..9411..7116..9718..6882
%C A214510 .8...18630.24035.23979.23261.26077.20216.26479.20016
%C A214510 .9...50775.65977.66474.63790.72137.55400.71469.55907.69764.57274
%C A214510 where k indicates the position of a node in the quarter-rectangle.
%C A214510 For each n, the maximum value of k is 2*floor((n+1)/2).
%C A214510 Reading this array by rows gives the sequence.
%H A214510 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 A214510 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 A214510 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 A214510 N   0  1  2  3
%e A214510     4  5  6  7
%e A214510 NT 23 24 24 23
%e A214510    23 24 24 23
%e A214510 To limit duplication, only the top left-hand corner 23 and the 24 to its right are stored in the sequence,
%e A214510 i.e. T(2,1) = 23 and T(2,2) = 24.
%Y A214510 Cf. A213106, A213249, A213342, A214022, A214122, A214397, A214399, A214504
%K A214510 nonn,tabf
%O A214510 2,1
%A A214510 _Christopher Hunt Gribble_, Jul 19 2012
%E A214510 Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012