A214503 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 7, n >= 2.

113, 116, 116, 122, 906, 1028, 1050, 1088, 1016, 1152, 1020, 980, 6751, 8562, 9411, 9718, 8651, 8317, 7116, 6882, 50036, 69029, 80263, 82942, 71736, 67670, 61229, 60116, 81276, 63148, 46550, 44196, 335569, 482769, 577787, 600124, 494659, 488710, 465142, 458850, 599448, 463257, 353704, 341918

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......113....116....116....122

.3......906...1028...1050...1088...1016...1152...1020....980

.4.....6751...8562...9411...9718...8651...8317...7116...6882

.5....50036..69029..80263..82942..71736..67670..61229..60116..81276..63148..46550..44196

.6...335569.482769.577787.600124.494659.488710.465142.458850.599448.463257.353704.341918

where k indicates the position of a 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 (N) occurs in a complete non-self-adjacent simple path is
N    0   1   2   3   4   5   6
     7   8   9  10  11  12  13
NT 113 116 116 122 116 116 113
   113 116 116 122 116 116 113
To limit duplication, only the top left-hand corner 113 and the 116, 116, 122 to its right are stored in the sequence,
i.e. T(2,1) = 113, T(2,2) = 116, T(2,3) = 116 and T(2,4) = 122.

Crossrefs

Cf. A213106, A213249, A213383, A214037, A214373, A214397, A214399, A214504, A214510, A214563, A214601

Sequence in context: A204377 A242557 A345072 * A054033 A167843 A159466

Adjacent sequences: A214500 A214501 A214502 * A214504 A214505 A214506

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 22 2012

Status

approved