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A214025 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 6, n >= 2. 5
13, 10, 8, 77, 51, 38, 68, 36, 20, 330, 266, 248, 300, 145, 96, 1580, 1381, 1365, 1414, 813, 652, 1402, 596, 432, 7678, 6630, 6357, 6630, 3968, 3192, 6357, 3192, 2828, 35971, 30070, 27638, 30709, 18037, 13744, 27591, 14507, 13851, 26574, 15318, 17846 (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.......13....10.....8

..3.......77....51....38....68....36....20

..4......330...266...248...300...145....96

..5.....1580..1381..1365..1414...813...652..1402...596...432

..6.....7678..6630..6357..6630..3968..3192..6357..3192..2828

..7....35971.30070.27638.30709.18037.13744.27591.14507.13851.26574.15318.17846

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.

LINKS

Table of n, a(n) for n=2..46.

C. H. Gribble, Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.

C. H. Gribble, Computes characteristics of complete non-self-adjacent 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 non-self-adjacent simple path is

SN  0  1  2  3  4  5

    6  7  8  9 10 11

NT 13 10  8  8 10 13

   13 10  8  8 10 13

To limit duplication, only the top left-hand corner 13 and the 10 and 8 to its right are stored in the sequence, i.e. T(2,1) = 13, T(2,2) = 10 and T(2,3) = 8.

CROSSREFS

Cf. A213106, A213249, A213375, A213478, A213954, A214022, A214023

Sequence in context: A206609 A281085 A072270 * A240812 A291425 A180864

Adjacent sequences:  A214022 A214023 A214024 * A214026 A214027 A214028

KEYWORD

nonn,tabf

AUTHOR

Christopher Hunt Gribble, Jul 01 2012

STATUS

approved

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Last modified January 19 00:40 EST 2020. Contains 331030 sequences. (Running on oeis4.)