A214022 - OEIS

%I #9 Jul 03 2012 15:55:51

%S 5,5,17,12,14,10,46,37,37,18,122,110,102,52,94,32,330,300,266,145,248,

%T 96,888,780,695,385,607,258,602,270,2347,2008,1842,1001,1526,663,1387,

%U 669,6115,5170,4840,2597,3979,1718,3349,1595,3076,1564,15811,13288,12545,6722,10331,4481,8461,3925,7181,3556

%N Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2.

%C 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.

%C The quarter-rectangle is read by rows.

%C The irregular array of numbers is:

%C ....k......1.....2.....3.....4.....5.....6.....7.....8.....9....10

%C ..n

%C ..2........5.....5

%C ..3.......17....12....14....10

%C ..4.......46....37....37....18

%C ..5......122...110...102....52....94....32

%C ..6......330...300...266...145...248....96

%C ..7......888...780...695...385...607...258...602...270

%C ..8.....2347..2008..1842..1001..1526...663..1387...669

%C ..9.....6115..5170..4840..2597..3979..1718..3349..1595..3076..1564

%C .10....15811.13288.12545..6722.10331..4481..8461..3925..7181..3556

%C where k indicates the position of the start node in the quarter-rectangle.

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

%C Reading this array by rows gives the sequence.

%H C. H. Gribble, <a href="https://oeis.org/wiki/Complete_non-self-adjacent_paths:Results_for_Square_Lattice">Computed characteristics of complete non-self-adjacent paths in a square lattice bounded by various sizes of rectangle.</a>

%H C. H. Gribble, <a href="https://oeis.org/wiki/Complete non-self-adjacent paths:Program">Computes characteristics of complete non-self-adjacent paths in square and cubic lattices bounded by various sizes of rectangle and rectangular cuboid respectively.</a>

%e When n = 2, the number of times (NT) each node in the rectangle is the start node (SN) of a complete non-self-adjacent simple path is

%e SN 0 1 2 3

%e    4 5 6 7

%e NT 5 5 5 5

%e    5 5 5 5

%e To limit duplication, only the top left-hand corner 5 and the 5 to its right are stored in the sequence, i.e. T(2,1) = 5 and T(2,2) = 5.

%Y Cf. A213106, A213249, A213342, A213478, A213954

%K nonn,tabf

%O 2,1

%A _Christopher Hunt Gribble_, Jul 01 2012