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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
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.
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
KEYWORD
nonn,tabf
AUTHOR
EXTENSIONS
Comment corrected by Christopher Hunt Gribble, Jul 22 2012
STATUS
approved