A214608 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 9, n >= 2.

304, 310, 314, 334, 334, 4137, 4754, 4811, 4929, 4920, 4610, 5260, 4738, 4784, 4924, 50775, 66474, 72137, 71469, 69764, 65977, 63790, 55400, 55907, 57274, 676474, 969677, 1118226, 1096104, 1058044, 1003962, 946620, 864012, 870946, 884912, 1154902, 887242, 651592, 669896, 710904

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 5 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......13......14......15

.n

.2......304.....310.....314.....334.....334

.3.....4137....4754....4811....4929....4920....4610....5260....4738....4784....4924

.4....50775...66474...72137...71469...69764...65977...63790...55400...55907...57274

.5...676474..969677.1118226.1096104.1058044.1003962..946620..864012..870946..884912.1154902..887242..651592..669896..710904

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

For each n, the maximum value of k is 5*floor((n+1)/2).

Reading this array by rows gives the sequence.

Links

Table of n, a(n) for n=2..41.

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  14  15  16  17
NT 304 310 314 334 334 334 314 310 304
   304 310 314 334 334 334 314 310 304
To limit duplication, only the top left-hand corner 304 and the 310, 314, 334, 334 to its right are stored in the sequence,
i.e. T(2,1) = 304, T(2,2) = 310, T(2,3) = 314, T(2,4) = 334 and T(2,5) = 334.

Crossrefs

Cf. A213106, A213249, A213426, A214042, A214376, A214397, A214399, A214504, A214510, A214563, A214601, A214503, A214605

Sequence in context: A291132 A328277 A253394 * A158932 A270303 A187934

Adjacent sequences: A214605 A214606 A214607 * A214609 A214610 A214611

Keyword

nonn,tabf

Author

Christopher Hunt Gribble, Jul 22 2012

Status

approved