

A214399


Irregular array T(n,k) of the numbers of nonextendable (complete) nonselfadjacent simple paths incorporating each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 2, n >= 2.


7



6, 12, 14, 23, 24, 40, 42, 40, 68, 70, 70, 113, 116, 116, 122, 186, 190, 192, 202, 304, 310, 314, 334, 334, 495, 504, 512, 546, 552, 804, 818, 832, 890, 902, 912, 1304, 1326, 1350, 1446, 1470, 1490, 2113, 2148, 2188, 2346, 2388, 2428, 2434, 3422, 3478, 3544, 3802, 3874, 3944, 3966
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OFFSET

2,1


COMMENTS

The subset of nodes is contained in the top lefthand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 1 to capture all geometrically distinct counts.
The quarterrectangle is read by rows.
The irregular array of numbers is:
....k....1....2....3....4....5....6....7....8....9...10
..n
..2......6
..3.....12...14
..4.....23...24
..5.....40...42...40
..6.....68...70...70
..7....113..116..116..122
..8....186..190..192..202
..9....304..310..314..334..334
.10....495..504..512..546..552
.11....804..818..832..890..902..912
.12...1304.1326.1350.1446.1470.1490
.13...2113.2148.2188.2346.2388.2428.2434
.14...3422.3478.3544.3802.3874.3944.3966
.15...5540.5630.5738.6158.6278.6398.6442.6462
where k indicates the position of a node in the quarterrectangle.
For each n, the maximum value of k is floor((n+1)/2).
Reading this array by rows gives the sequence.


LINKS

Table of n, a(n) for n=2..56.
C. H. Gribble, Computed characteristics of complete nonselfadjacent paths in a square lattice bounded by various sizes of rectangle.
C. H. Gribble, Computes characteristics of complete nonselfadjacent 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 (N) occurs in a complete nonselfadjacent simple path is
N 0 1
2 3
NT 6 6
6 6
To limit duplication, only the top lefthand corner 6 is stored in the sequence, i.e. T(2,1) = 6.


CROSSREFS

Cf. A213106, A213249, A213274, A213478, A214119, A214397.
Sequence in context: A315612 A315613 A246590 * A079946 A315614 A118586
Adjacent sequences: A214396 A214397 A214398 * A214400 A214401 A214402


KEYWORD

nonn,tabf


AUTHOR

Christopher Hunt Gribble, Jul 15 2012


EXTENSIONS

Corrected by Christopher Hunt Gribble, Jul 19 2012


STATUS

approved



