A214563 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 5, n >= 2.

40, 42, 40, 188, 209, 204, 210, 228, 204, 820, 1007, 1058, 1008, 907, 776, 3426, 4601, 5076, 4601, 4104, 3608, 5076, 3608, 2608, 13344, 18726, 21050, 18302, 17364, 15896, 21307, 15275, 11148, 50036, 71736, 81276, 69029, 67670, 63148, 80263, 61229, 46550, 82942, 60116, 44196

Offset: 2

Author

Christopher Hunt Gribble, Jul 21 2012

Keywords

• nonn
• tabf

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......40....42....40

.3.....188...209...204...210...228...204

.4.....820..1007..1058..1008...907...776

.5....3426..4601..5076..4601..4104..3608..5076..3608..2608

.6...13344.18726.21050.18302.17364.15896.21307.15275.11148

.7...50036.71736.81276.69029.67670.63148.80263.61229.46550.82942.60116.44196

where k indicates the position of a 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.

Examples

			When n = 2, the number of times (NT) each node in the rectangle (N) occurs in a complete non-self-adjacent simple path is
N   0  1  2  3  4
    5  6  7  8  9
NT 40 42 40 42 40
   40 42 40 42 40
To limit duplication, only the top left-hand corner 40 and the 42 and 40 to its right are stored in the sequence,
i.e. T(2,1) = 40, T(2,2) = 42 and T(2,3) = 40.
		

Links

• 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.

Crossrefs

Cf. A213106, A213249, A213375, A214023, A214359, A214397, A214399, A214504, A214510

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012