cp's OEIS Frontend

A214601 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.

%I A214601 #4 Jul 23 2012 12:48:12
%S A214601 68,70,70,418,472,479,470,524,452,2401,3013,3312,3043,2844,2375,13344,
%T A214601 18302,21307,18726,17364,15275,21050,15896,11148,68230,98032,117197,
%U A214601 98032,95942,89083,117197,89083,64506,335569,494659,599448,482769,488710,463257,577787,465142,353704,600124,458850,341918
%N A214601 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 A214601 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 A214601 The quarter-rectangle is read by rows.
%C A214601 The irregular array of numbers is:
%C A214601 ...k......1......2......3......4......5......6......7......8......9.....10.....11.....12
%C A214601 .n
%C A214601 .2.......68.....70.....70
%C A214601 .3......418....472....479....470....524....452
%C A214601 .4.....2401...3013...3312...3043...2844...2375
%C A214601 .5....13344..18302..21307..18726..17364..15275..21050..15896..11148
%C A214601 .6....68230..98032.117197..98032..95942..89083.117197..89083..64506
%C A214601 .7...335569.494659.599448.482769.488710.463257.577787.465142.353704.600124.458850.341918
%C A214601 where k indicates the position of a node in the quarter-rectangle.
%C A214601 For each n, the maximum value of k is 3*floor((n+1)/2).
%C A214601 Reading this array by rows gives the sequence.
%H A214601 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 A214601 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 A214601 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 A214601 N   0  1  2  3  4  5
%e A214601     6  7  8  9 10 11
%e A214601 NT 68 70 70 70 70 68
%e A214601    68 70 70 70 70 68
%e A214601 To limit duplication, only the top left-hand corner 68 and the two 70's to its right are stored in the sequence,
%e A214601 i.e. T(2,1) = 68, T(2,2) = 70 and T(2,3) = 70.
%Y A214601 Cf. A213106, A213249, A213379, A214025, A213070, A214397, A214399, A214504, A214510, A214563
%K A214601 nonn,tabf
%O A214601 2,1
%A A214601 _Christopher Hunt Gribble_, Jul 22 2012