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A213070 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 6, n >= 2. 4
31, 0, 0, 165, 27, 32, 8, 0, 0, 720, 187, 236, 104, 30, 108, 3431, 992, 1179, 746, 251, 580, 920, 352, 1210, 16608, 4361, 5027, 4361, 1094, 2043, 5027, 2043, 6268, 76933, 17601, 20009, 21068, 3675, 7213, 26181, 9258, 26414, 25090, 10048, 32132 (list; graph; refs; listen; history; text; internal format)
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......31.....0.....0
.3.....165....27....32.....8.....0.....0
.4.....720...187...236...104....30...108
.5....3431...992..1179...746...251...580...920...352..1210
.6...16608..4361..5027..4361..1094..2043..5027..2043..6268
.7...76933.17601.20009.21068..3675..7213.26181..9258.26414.25090.10048.32132
where k indicates the position of the end 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.
LINKS
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
NT 31 0 0 0 0 31
31 0 0 0 0 31
To limit duplication, only the top left-hand corner 31 and the two zeros to its right are stored in the sequence, i.e. T(2,1) = 31, T(2,2) = 0 and T(2,3) = 0.
CROSSREFS
Sequence in context: A028363 A091511 A324684 * A221432 A085012 A086019
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
Comment corrected by Christopher Hunt Gribble, Jul 22 2012
STATUS
approved

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Last modified July 20 04:43 EDT 2024. Contains 374441 sequences. (Running on oeis4.)