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

2,1

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......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.

Links

Table of n, a(n) for n=2..46.

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 (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.

Crossrefs

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

Sequence in context: A007634 A228184 A128843 * A111167 A070980 A131535

Adjacent sequences: A214560 A214561 A214562 * A214564 A214565 A214566

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 21 2012

Extensions

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

Status

approved