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A214023
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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 5, n >= 2.
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6
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8, 7, 6, 36, 25, 20, 32, 18, 12, 122, 102, 94, 110, 52, 32, 436, 395, 394, 395, 220, 154, 394, 154, 80, 1580, 1414, 1402, 1381, 813, 596, 1365, 652, 432, 5600, 4829, 4650, 4795, 2792, 2036, 4453, 2285, 1712, 4412, 2556, 2248, 19287, 16131, 15246, 16735, 9444, 6758, 15113, 7697, 5858, 13878, 8612, 8496
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OFFSET
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2,1
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COMMENTS
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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........8.....7.....6
..3.......36....25....20....32....18....12
..4......122...102....94...110....52....32
..5......436...395...394...395...220...154...394...154....80
..6.....1580..1414..1402..1381...813...596..1365...652...432
..7.....5600..4829..4650..4795..2792..2036..4453..2285..1712..4412..2556..2248
..8....19287.16131.15246.16735..9444..6758.15113..7697..5858.13878..8612..8496
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.
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LINKS
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EXAMPLE
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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
NT 8 7 6 7 8
8 7 6 7 8
To limit duplication, only the top left-hand corner 8 and the 7 and 6 to its right are stored in the sequence, i.e. T(2,1) = 8, T(2,2) = 7 and T(2,3) = 6.
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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