A214397 Triangle T(n,k) of the numbers of nodes in all non-extendable (complete) non-self-adjacent simple paths within a square lattice bounded by rectangles with nodal dimensions n and k, n >= k >= 2.

24, 76, 320, 188, 1040, 4608, 408, 2756, 18636, 104272, 832, 8368, 67952, 513460, 3349208, 1624, 21468, 228432, 2312112, 19845964, 152434216, 3080, 53108, 730772, 9943160, 113061272, 1125079096, 10676325280, 5716, 128072, 2261792, 41508164, 629214072, 8150708696, 99701732480, 1200653865056

Offset

2,1

Comments

The triangle of numbers is:

....k.....2......3.......4........5.........6..........7...........8.............9

.n

.2.......24

.3.......76....320

.4......188...1040....4608

.5......408...2756...18636...104272

.6......832...8368...67952...513460...3349208

.7.....1624..21468..228432..2312112..19845964..152434216

.8.....3080..53108..730772..9943160.113061272.1125079096.10676325280

.9.....5716.128072.2261792.41508164.629214072.8150708696.99701732480.1200653865056

Reading this triangle by rows gives the sequence.

Links

Table of n, a(n) for n=2..37.

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

T(2,2) = The number of nodes in all complete non-self-adjacent simple paths within a 2 X 2 node rectangle.

Crossrefs

Cf. A213106, A213249.

Sequence in context: A211574 A211588 A211596 * A048352 A144459 A290710

Adjacent sequences: A214394 A214395 A214396 * A214398 A214399 A214400

Keyword

nonn,tabl

Author

Christopher Hunt Gribble, Jul 15 2012

Status

approved