

A214023


Irregular array T(n,k) of the numbers of nonextendable (complete) nonselfadjacent 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.


6



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

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........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 quarterrectangle.
For each n, the maximum value of k is 3*floor((n+1)/2).
Reading this array by rows gives the sequence.


LINKS

Table of n, a(n) for n=2..58.
C. H. Gribble, Computed characteristics of complete nonselfadjacent paths in a square lattice bounded by various sizes of rectangle.
C. H. Gribble, Computes characteristics of complete nonselfadjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.


EXAMPLE

When n = 2, the number of times (NT) each node in the rectangle is the start node (SN) of a complete nonselfadjacent 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 lefthand 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.


CROSSREFS

Cf. A213106, A213249, A213375, A213478, A213954, A214022
Sequence in context: A132037 A247095 A124597 * A154209 A115373 A021118
Adjacent sequences: A214020 A214021 A214022 * A214024 A214025 A214026


KEYWORD

nonn,tabf


AUTHOR

Christopher Hunt Gribble, Jul 01 2012


STATUS

approved



