

A214608


Irregular array T(n,k) of the numbers of nonextendable (complete) nonselfadjacent 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.


0



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
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OFFSET

2,1


COMMENTS

The subset of nodes is contained in the top lefthand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 5 to capture all geometrically distinct counts.
The quarterrectangle 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 quarterrectangle.
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 nonselfadjacent paths in a square lattice bounded by various sizes of rectangle.
C. H. Gribble, Computes characteristics of complete nonselfadjacent 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 nonselfadjacent 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 lefthand 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: A236813 A291132 A253394 * A158932 A270303 A187934
Adjacent sequences: A214605 A214606 A214607 * A214609 A214610 A214611


KEYWORD

nonn,tabf


AUTHOR

Christopher Hunt Gribble, Jul 22 2012


STATUS

approved



