cp's OEIS Frontend

A214563 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 5, n >= 2.

%I A214563 #7 Jul 23 2012 12:47:42
%S A214563 40,42,40,188,209,204,210,228,204,820,1007,1058,1008,907,776,3426,
%T A214563 4601,5076,4601,4104,3608,5076,3608,2608,13344,18726,21050,18302,
%U A214563 17364,15896,21307,15275,11148,50036,71736,81276,69029,67670,63148,80263,61229,46550,82942,60116,44196
%N A214563 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 5, n >= 2.
%C A214563 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 A214563 The quarter-rectangle is read by rows.
%C A214563 The irregular array of numbers is:
%C A214563 ...k.....1.....2.....3.....4.....5.....6.....7.....8.....9....10....11....12
%C A214563 .n
%C A214563 .2......40....42....40
%C A214563 .3.....188...209...204...210...228...204
%C A214563 .4.....820..1007..1058..1008...907...776
%C A214563 .5....3426..4601..5076..4601..4104..3608..5076..3608..2608
%C A214563 .6...13344.18726.21050.18302.17364.15896.21307.15275.11148
%C A214563 .7...50036.71736.81276.69029.67670.63148.80263.61229.46550.82942.60116.44196
%C A214563 where k indicates the position of a node in the quarter-rectangle.
%C A214563 For each n, the maximum value of k is 3*floor((n+1)/2).
%C A214563 Reading this array by rows gives the sequence.
%H A214563 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 A214563 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 A214563 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 A214563 N   0  1  2  3  4
%e A214563     5  6  7  8  9
%e A214563 NT 40 42 40 42 40
%e A214563    40 42 40 42 40
%e A214563 To limit duplication, only the top left-hand corner 40 and the 42 and 40 to its right are stored in the sequence,
%e A214563 i.e. T(2,1) = 40, T(2,2) = 42 and T(2,3) = 40.
%Y A214563 Cf. A213106, A213249, A213375, A214023, A214359, A214397, A214399, A214504, A214510
%K A214563 nonn,tabf
%O A214563 2,1
%A A214563 _Christopher Hunt Gribble_, Jul 21 2012
%E A214563 Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012