A214042 - OEIS

%I #12 Jul 23 2012 12:45:17

%S 55,36,24,18,16,732,476,294,197,168,628,302,148,82,64,6115,4840,3979,

%T 3349,3076,5170,2597,1718,1595,1564,64904,57210,52820,46787,43294,

%U 53478,31544,26459,28472,28700,50228,22432,19802,27924,30696

%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 9, 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 5 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....11....12....13....14....15

%C .n

%C .2......55....36....24....18....16

%C .3.....732...476...294...197...168...628...302...148....82....64

%C .4....6115..4840..3979..3349..3076..5170..2597..1718..1595..1564

%C .5...64904.57210.52820.46787.43294.53478.31544.26459.28472.28700.50228.22432.19802.27924.30696

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

%C For each n, the maximum value of k is 5*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  4  5  6  7  8

%e     9 10 11 12 13 14 15 16 17

%e NT 55 36 24 18 16 18 24 36 55

%e    55 36 24 18 16 18 24 36 55

%e To limit duplication, only the top left-hand corner 34 and the 23, 16 and 13 to its right are stored in the sequence, i.e. T(2,1) = 34, T(2,2) = 23, T(2,3) = 16 and T(2,4) = 13.

%Y Cf. A213106, A213249, A213426, A213478, A213954, A214022, A214023, A214025, A214037, A214038

%K nonn,tabf

%O 2,1

%A _Christopher Hunt Gribble_, Jul 01 2012

%E Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012