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A214025
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 6, n >= 2.
5
13, 10, 8, 77, 51, 38, 68, 36, 20, 330, 266, 248, 300, 145, 96, 1580, 1381, 1365, 1414, 813, 652, 1402, 596, 432, 7678, 6630, 6357, 6630, 3968, 3192, 6357, 3192, 2828, 35971, 30070, 27638, 30709, 18037, 13744, 27591, 14507, 13851, 26574, 15318, 17846
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 3 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.......13....10.....8
..3.......77....51....38....68....36....20
..4......330...266...248...300...145....96
..5.....1580..1381..1365..1414...813...652..1402...596...432
..6.....7678..6630..6357..6630..3968..3192..6357..3192..2828
..7....35971.30070.27638.30709.18037.13744.27591.14507.13851.26574.15318.17846
where k indicates the position of the start node in the quarter-rectangle.
For each n, the maximum value of k is 3*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 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
NT 13 10 8 8 10 13
13 10 8 8 10 13
To limit duplication, only the top left-hand corner 13 and the 10 and 8 to its right are stored in the sequence, i.e. T(2,1) = 13, T(2,2) = 10 and T(2,3) = 8.
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved