

A213070


Irregular array T(n,k) of the numbers of nonextendable (complete) nonselfadjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 6, n >= 2.


4



31, 0, 0, 165, 27, 32, 8, 0, 0, 720, 187, 236, 104, 30, 108, 3431, 992, 1179, 746, 251, 580, 920, 352, 1210, 16608, 4361, 5027, 4361, 1094, 2043, 5027, 2043, 6268, 76933, 17601, 20009, 21068, 3675, 7213, 26181, 9258, 26414, 25090, 10048, 32132
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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 3 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
.n
.2......31.....0.....0
.3.....165....27....32.....8.....0.....0
.4.....720...187...236...104....30...108
.5....3431...992..1179...746...251...580...920...352..1210
.6...16608..4361..5027..4361..1094..2043..5027..2043..6268
.7...76933.17601.20009.21068..3675..7213.26181..9258.26414.25090.10048.32132
where k indicates the position of the end node in the quarterrectangle.
For each n, the maximum value of k is 3*floor((n+1)/2).
Reading this array by rows gives the sequence.


LINKS



EXAMPLE

When n = 2, the number of times (NT) each node in the rectangle is the end node (EN) of a complete nonselfadjacent simple path is
EN 0 1 2 3 4 5
6 7 8 9 10 11
NT 31 0 0 0 0 31
31 0 0 0 0 31
To limit duplication, only the top lefthand corner 31 and the two zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0 and T(2,3) = 0.


CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



EXTENSIONS



STATUS

approved



