cp's OEIS Frontend

A213089 Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 3, n >= 2.

%I A213089 #31 Jun 22 2012 13:17:01
%S A213089 4,4,2,4,8,12,0,8,4,8,16,18,14,8,14,4,8,16,22,42,24,42,22,18,4,8,16,
%T A213089 22,48,60,82,90,66,34,24,2,4,8,16,22,50,66,132,160,218,120,122,56,36,
%U A213089 4,4,8,16,22,52,68,144,222,334,406,302,288,198,88,52,6,4,8,16,22,54,70,152,238,416,574,810,642,760,456,320,136,72,8
%N A213089 Irregular array T(n,k) of numbers/2 of non-extendable (complete) non-self-adjacent simple paths of each length within a square lattice bounded by rectangles with nodal dimensions n and 3, n >= 2.
%C A213089 The irregular array of numbers is:
%C A213089 ...k..3...4...5...6...7...8...9..10..11..12..13..14..15..16..17..18..19..20
%C A213089 .n
%C A213089 .2....4...4...2
%C A213089 .3....4...8..12...0...8
%C A213089 .4....4...8..16..18..14...8..14
%C A213089 .5....4...8..16..22..42..24..42..22..18
%C A213089 .6....4...8..16..22..48..60..82..90..66..34..24...2
%C A213089 .7....4...8..16..22..50..66.132.160.218.120.122..56..36...4
%C A213089 .8....4...8..16..22..52..68.144.222.334.406.302.288.198..88..52...6
%C A213089 .9....4...8..16..22..54..70.152.238.416..74.810.642.760.456.320.136..72...8
%C A213089 where k is the path length in nodes. In an attempt to define the irregularity of the array, it appears that the maximum value of k is 2n+1 for 2 <= n <= 6 and 2n+2 for n >= 7. Reading this array by rows gives the sequence. One half of the numbers of paths constitute the sequence to remove the effect of the bilateral symmetry of the rectangle.
%H A213089 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 A213089 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 A213089 T(2,3) = One half of the number of complete non-self-adjacent simple paths of length 3 nodes within a square lattice bounded by a 2 X 3 node rectangle.
%Y A213089 Cf. A213106, A213249, A213274.
%K A213089 nonn,tabf
%O A213089 2,1
%A A213089 _Christopher Hunt Gribble_, Jun 08 2012