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A214375
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 8, n >= 2.
2
86, 0, 0, 0, 747, 119, 124, 109, 12, 0, 0, 0, 5029, 1245, 1624, 1537, 386, 106, 618, 898, 40489, 11359, 15642, 15239, 6345, 1689, 6165, 8214, 7544, 2772, 12824, 16728, 343645, 89102, 125043, 128224, 72452, 12593, 39711, 47539, 80324, 28387, 113790, 134553
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 4 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.......86......0......0......0
.3......747....119....124....109.....12......0......0......0
.4.....5029...1245...1624...1537....386....106....618....898
.5....40489..11359..15642..15239...6345...1689...6165...8214...7544...2772..12824..16728
.6...343645..89102.125043.128224..72452..12593..39711..47539..80324..28387.113790.134553
where k indicates the position of the end node in the quarter-rectangle.
For each n, the maximum value of k is 4*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
NT 86 0 0 0 0 0 0 86
86 0 0 0 0 0 0 86
To limit duplication, only the top left-hand corner 86 and the three zeros to its right are stored in the sequence, i.e. T(2,1) = 86, T(2,2) = 0, T(2,3) = 0 and T(2,4) = 0.
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
Comment corrected by Christopher Hunt Gribble, Jul 22 2012
STATUS
approved