

A214042


Irregular array T(n,k) of the numbers of nonextendable (complete) nonselfadjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 9, n >= 2.


2



55, 36, 24, 18, 16, 732, 476, 294, 197, 168, 628, 302, 148, 82, 64, 6115, 4840, 3979, 3349, 3076, 5170, 2597, 1718, 1595, 1564, 64904, 57210, 52820, 46787, 43294, 53478, 31544, 26459, 28472, 28700, 50228, 22432, 19802, 27924, 30696
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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......55....36....24....18....16
.3.....732...476...294...197...168...628...302...148....82....64
.4....6115..4840..3979..3349..3076..5170..2597..1718..1595..1564
.5...64904.57210.52820.46787.43294.53478.31544.26459.28472.28700.50228.22432.19802.27924.30696
where k indicates the position of the start 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 is the start node (SN) of a complete nonselfadjacent simple path is
SN 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
NT 55 36 24 18 16 18 24 36 55
55 36 24 18 16 18 24 36 55
To limit duplication, only the top lefthand 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.


CROSSREFS

Cf. A213106, A213249, A213426, A213478, A213954, A214022, A214023, A214025, A214037, A214038
Sequence in context: A178509 A033375 A236416 * A112892 A232653 A291502
Adjacent sequences: A214039 A214040 A214041 * A214043 A214044 A214045


KEYWORD

nonn,tabf


AUTHOR

Christopher Hunt Gribble, Jul 01 2012


EXTENSIONS

Comment corrected by Christopher Hunt Gribble, Jul 22 2012


STATUS

approved



