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A214375 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 8, n >= 2. 2
86, 0, 0, 0, 747, 119, 124, 109, 12, 0, 0, 0, 5029, 1245, 1624, 1537, 386, 106, 618, 898, 40489, 11359, 15642, 15239, 6345, 1689, 6165, 8214, 7544, 2772, 12824, 16728, 343645, 89102, 125043, 128224, 72452, 12593, 39711, 47539, 80324, 28387, 113790, 134553 (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 4 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.......86......0......0......0

.3......747....119....124....109.....12......0......0......0

.4.....5029...1245...1624...1537....386....106....618....898

.5....40489..11359..15642..15239...6345...1689...6165...8214...7544...2772..12824..16728

.6...343645..89102.125043.128224..72452..12593..39711..47539..80324..28387.113790.134553

where k indicates the position of the end node in the quarter-rectangle.

For each n, the maximum value of k is 4*floor((n+1)/2).

Reading this array by rows gives the sequence.

LINKS

Table of n, a(n) for n=2..45.

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 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 12 13 14 15

NT 86  0  0  0  0  0  0 86

   86  0  0  0  0  0  0 86

To limit duplication, only the top left-hand corner 86 and the three zeros to its right are stored in the sequence, i.e. T(2,1) = 86, T(2,2) = 0, T(2,3) = 0 and T(2,4) = 0.

CROSSREFS

Cf. A213106, A213249, A213425, A214038, A214119, A214121, A214122, A214359, A213070, A214373.

Sequence in context: A172874 A316558 A172909 * A045916 A033406 A143759

Adjacent sequences:  A214372 A214373 A214374 * A214376 A214377 A214378

KEYWORD

nonn,tabf

AUTHOR

Christopher Hunt Gribble, Jul 14 2012

EXTENSIONS

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

STATUS

approved

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)