A214601 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 6, n >= 2.

68, 70, 70, 418, 472, 479, 470, 524, 452, 2401, 3013, 3312, 3043, 2844, 2375, 13344, 18302, 21307, 18726, 17364, 15275, 21050, 15896, 11148, 68230, 98032, 117197, 98032, 95942, 89083, 117197, 89083, 64506, 335569, 494659, 599448, 482769, 488710, 463257, 577787, 465142, 353704, 600124, 458850, 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 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.......68.....70.....70

.3......418....472....479....470....524....452

.4.....2401...3013...3312...3043...2844...2375

.5....13344..18302..21307..18726..17364..15275..21050..15896..11148

.6....68230..98032.117197..98032..95942..89083.117197..89083..64506

.7...335569.494659.599448.482769.488710.463257.577787.465142.353704.600124.458850.341918

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 10 11
NT 68 70 70 70 70 68
   68 70 70 70 70 68
To limit duplication, only the top left-hand corner 68 and the two 70's to its right are stored in the sequence,
i.e. T(2,1) = 68, T(2,2) = 70 and T(2,3) = 70.

Crossrefs

Cf. A213106, A213249, A213379, A214025, A213070, A214397, A214399, A214504, A214510, A214563

Sequence in context: A090493 A259081 A143737 * A043595 A043828 A043836

Adjacent sequences: A214598 A214599 A214600 * A214602 A214603 A214604

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 22 2012

Status

approved