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A214376
Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 9, n >= 2.
1
141, 0, 0, 0, 0, 1577, 247, 250, 206, 184, 14, 0, 0, 0, 0, 12996, 3061, 4080, 3938, 3744, 744, 206, 1502, 2186, 2196, 134159, 35481, 51391, 54213, 53870, 19468, 4934, 19662, 27966, 28436, 22132, 8396, 42588, 54710, 52792
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......141.....0.....0.....0.....0
.3.....1577...247...250...206...184....14.....0.....0.....0.....0
.4....12996..3061..4080..3938..3744...744...206..1502..2186..2196
.5...134159.35481.51391.54213.53870.19468..4934.19662.27966.28436.22132..8396.42588.54710.52792
where k indicates the position of the end 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.
EXAMPLE
When n = 2, the number of times (NT) each node in the rectangle is the end node (EN) of a complete non-self-adjacent simple path is
EN 0 1 2 3 4 5 6 7 8
9 10 11 12 13 14 15 16 17
NT 141 0 0 0 0 0 0 0 141
141 0 0 0 0 0 0 0 141
To limit duplication, only the top left-hand corner 141 and the four zeros to its right are stored in the sequence, i.e. T(2,1) = 141, T(2,2) = 0, T(2,3) = 0, T(2,4) = 0 and T(2,5) = 0.
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
Comment corrected by Christopher Hunt Gribble, Jul 22 2012
STATUS
approved