A214376 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 9, n >= 2.

141, 0, 0, 0, 0, 1577, 247, 250, 206, 184, 14, 0, 0, 0, 0, 12996, 3061, 4080, 3938, 3744, 744, 206, 1502, 2186, 2196, 134159, 35481, 51391, 54213, 53870, 19468, 4934, 19662, 27966, 28436, 22132, 8396, 42588, 54710, 52792

Offset

2,1

Comments

The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 5 to capture all geometrically distinct counts.

The quarter-rectangle is read by rows.

The irregular array of numbers is:

...k......1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12....13....14....15

.n

.2......141.....0.....0.....0.....0

.3.....1577...247...250...206...184....14.....0.....0.....0.....0

.4....12996..3061..4080..3938..3744...744...206..1502..2186..2196

.5...134159.35481.51391.54213.53870.19468..4934.19662.27966.28436.22132..8396.42588.54710.52792

where k indicates the position of the end node in the quarter-rectangle.

For each n, the maximum value of k is 5*floor((n+1)/2).

Reading this array by rows gives the sequence.

Links

Table of n, a(n) for n=2..41.

C. H. Gribble, Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.

C. H. Gribble, Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.

Example

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
EN   0   1   2   3   4   5   6   7   8
     9  10  11  12  13  14  15  16  17
NT 141   0   0   0   0   0   0   0 141
   141   0   0   0   0   0   0   0 141
To limit duplication, only the top left-hand corner 141 and the four zeros to its right are stored in the sequence, i.e. T(2,1) = 141, T(2,2) = 0, T(2,3) = 0, T(2,4) = 0 and T(2,5) = 0.

Crossrefs

Cf. A213106, A213249, A213426, A214042, A214119, A214121, A214122, A214359, A213070, A214373, A214375.

Sequence in context: A216729 A350614 A058939 * A165600 A137506 A036192

Adjacent sequences: A214373 A214374 A214375 * A214377 A214378 A214379

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 14 2012

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

Status

approved