A214038 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.

34, 23, 16, 13, 347, 225, 142, 109, 298, 146, 74, 46, 2347, 1842, 1526, 1387, 2008, 1001, 663, 669, 19287, 16735, 15113, 13878, 6131, 9444, 7697, 8612, 15246, 6758, 5858, 8496, 163666, 141849, 126129, 112049, 132636, 81112, 65551, 67006, 118724, 58677, 60918, 87046

Offset: 2

Author

Christopher Hunt Gribble, Jul 01 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 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.......34.....23.....16.....13

.3......347....225....142....109....298....146.....74.....46

.4.....2347...1842...1526...1387...2008...1001....663....669

.5....19287..16735..15113..13878...6131...9444...7697...8612..15246...6758...5858...8496

.6...163666.141849.126129.112049.132636..81112..65551..67006.118724..58677..60918..87046

where k indicates the position of the start 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.

Examples

			When n = 2, the number of times (NT) each node in the rectangle is the start node (SN) of a complete non-self-adjacent simple path is
SN  0  1  2  3  4  5  6  7
    8  9 10 11 12 13 14 15
NT 34 23 16 13 13 16 23 34
   34 23 16 13 13 16 23 34
To limit duplication, only the top left-hand corner 34 and the 23, 16 and 13 to its right are stored in the sequence, i.e. T(2,1) = 34, T(2,2) = 23, T(2,3) = 16 and T(2,4) = 13.
		

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, A213425, A213478, A213954, A214022, A214023, A214025, A214037