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A214022
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 4, n >= 2.
7
5, 5, 17, 12, 14, 10, 46, 37, 37, 18, 122, 110, 102, 52, 94, 32, 330, 300, 266, 145, 248, 96, 888, 780, 695, 385, 607, 258, 602, 270, 2347, 2008, 1842, 1001, 1526, 663, 1387, 669, 6115, 5170, 4840, 2597, 3979, 1718, 3349, 1595, 3076, 1564, 15811, 13288, 12545, 6722, 10331, 4481, 8461, 3925, 7181, 3556
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 2 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
..n
..2........5.....5
..3.......17....12....14....10
..4.......46....37....37....18
..5......122...110...102....52....94....32
..6......330...300...266...145...248....96
..7......888...780...695...385...607...258...602...270
..8.....2347..2008..1842..1001..1526...663..1387...669
..9.....6115..5170..4840..2597..3979..1718..3349..1595..3076..1564
.10....15811.13288.12545..6722.10331..4481..8461..3925..7181..3556
where k indicates the position of the start node in the quarter-rectangle.
For each n, the maximum value of k is 2*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
NT 5 5 5 5
5 5 5 5
To limit duplication, only the top left-hand corner 5 and the 5 to its right are stored in the sequence, i.e. T(2,1) = 5 and T(2,2) = 5.
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
STATUS
approved