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.

18, 0, 0, 75, 13, 16, 6, 0, 0, 256, 67, 88, 52, 14, 32, 932, 246, 308, 246, 80, 130, 308, 130, 288, 3431, 746, 920, 992, 251, 352, 1179, 580, 1210, 12027, 2143, 2612, 3522, 640, 954, 4399, 1941, 3956, 4170, 2394, 5136, 40489, 6345, 7544, 11359, 1689, 2772, 15642, 6165, 12824, 15239, 8214, 16728

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 3 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......18.....0.....0

.3......75....13....16.....6.....0.....0

.4.....256....67....88....52....14....32

.5.....932...246...308...246....80...130...308...130...288

.6....3431...746...920...992...251...352..1179...580..1210

.7...12027..2143..2612..3522...640...954..4399..1941..3956..4170..2394..5136

.8...40489..6345..7544.11359..1689..2772.15642..6165.12824.15239..8214.16728

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

For each n, the maximum value of k is 3*floor((n+1)/2).

Reading this array by rows gives the sequence.

Links

Table of n, a(n) for n=2..58.

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
NT 18  0  0  0 18
   18  0  0  0 18
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.

Crossrefs

Cf. A213106, A213249, A213375, A214023, A214119, A214121, A214122.

Sequence in context: A156400 A008424 A023920 * A198810 A347532 A243911

Adjacent sequences: A214356 A214357 A214358 * A214360 A214361 A214362

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 13 2012

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

Status

approved