Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #4 Jul 23 2012 12:48:12
%S 68,70,70,418,472,479,470,524,452,2401,3013,3312,3043,2844,2375,13344,
%T 18302,21307,18726,17364,15275,21050,15896,11148,68230,98032,117197,
%U 98032,95942,89083,117197,89083,64506,335569,494659,599448,482769,488710,463257,577787,465142,353704,600124,458850,341918
%N Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths incorporating each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 6, 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 3 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
%C .n
%C .2.......68.....70.....70
%C .3......418....472....479....470....524....452
%C .4.....2401...3013...3312...3043...2844...2375
%C .5....13344..18302..21307..18726..17364..15275..21050..15896..11148
%C .6....68230..98032.117197..98032..95942..89083.117197..89083..64506
%C .7...335569.494659.599448.482769.488710.463257.577787.465142.353704.600124.458850.341918
%C where k indicates the position of a node in the quarter-rectangle.
%C For each n, the maximum value of k is 3*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 (N) occurs in a complete non-self-adjacent simple path is
%e N 0 1 2 3 4 5
%e 6 7 8 9 10 11
%e NT 68 70 70 70 70 68
%e 68 70 70 70 70 68
%e To limit duplication, only the top left-hand corner 68 and the two 70's to its right are stored in the sequence,
%e i.e. T(2,1) = 68, T(2,2) = 70 and T(2,3) = 70.
%Y Cf. A213106, A213249, A213379, A214025, A213070, A214397, A214399, A214504, A214510, A214563
%K nonn,tabf
%O 2,1
%A _Christopher Hunt Gribble_, Jul 22 2012