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.

52, 0, 0, 0, 353, 57, 62, 60, 10, 0, 0, 0, 1931, 495, 622, 602, 200, 56, 262, 364, 12027, 3522, 4399, 4170, 2143, 640, 1941, 2394, 2612, 954, 3956, 5136, 76933, 21068, 26181, 25090, 17601, 3675, 9258, 10048, 20009, 7213, 26414, 32132

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 4 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

.n

.2......52.....0.....0.....0

.3.....353....57....62....60....10.....0.....0.....0

.4....1931...495...622...602...200....56...262...364

.5...12027..3522..4399..4170..2143...640..1941..2394..2612...954..3956..5136

.6...76933.21068.26181.25090.17601..3675..9258.10048.20009..7213.26414.32132

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

For each n, the maximum value of k is 4*floor((n+1)/2).

Reading this array by rows gives the sequence.

Links

Table of n, a(n) for n=2..45.

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
NT 52  0  0  0  0  0 52
   52  0  0  0  0  0 52
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.

Crossrefs

Cf. A213106, A213249, A213383, A214037, A214119, A214121, A214122, A214359, A213070.

Sequence in context: A172695 A172786 A324683 * A230299 A308235 A022079

Adjacent sequences: A214370 A214371 A214372 * A214374 A214375 A214376

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 14 2012

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

Status

approved