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A214122 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 4, n >= 2. 6
10, 0, 33, 6, 4, 0, 90, 22, 22, 4, 256, 52, 67, 14, 88, 32, 720, 104, 187, 30, 236, 108, 1931, 200, 495, 56, 622, 262, 602, 364, 5029, 386, 1245, 106, 1624, 618, 1537, 898, 12996, 744, 3061, 206, 4080, 1502, 3938, 2186, 3744, 2196, 33512, 1422, 7615, 398 (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 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......10.....0

..3......33.....6.....4.....0

..4......90....22....22.....4

..5.....256....52....67....14....88....32

..6.....720...104...187....30...236...108

..7....1931...200...495....56...622...262...602...364

..8....5029...386..1245...106..1624...618..1537...898

..9...12996...744..3061...206..4080..1502..3938..2186..3744..2196

.10...33512..1422..7615...398.10014..3676..9775..5466..9177..5246

where k indicates the position of the end 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.

LINKS

Table of n, a(n) for n=2..53.

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

NT 10  0  0 10

   10  0  0 10

To limit duplication, only the top left-hand corner 10 and the 0 to its right are stored in the sequence, i.e. T(2,1) = 10 and T(2,2) = 0.

CROSSREFS

Cf. A213106, A213249, A213342, A214022, A214119, A214121.

Sequence in context: A171809 A167302 A302576 * A084033 A261943 A062255

Adjacent sequences:  A214119 A214120 A214121 * A214123 A214124 A214125

KEYWORD

nonn,tabf

AUTHOR

Christopher Hunt Gribble, Jul 04 2012

EXTENSIONS

Comment corrected by Christopher Hunt Gribble, Jul 22 2012

STATUS

approved

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Last modified May 24 17:16 EDT 2019. Contains 323533 sequences. (Running on oeis4.)