cp's OEIS Frontend

A214122 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2.

%I A214122 #9 Jul 23 2012 12:45:56
%S A214122 10,0,33,6,4,0,90,22,22,4,256,52,67,14,88,32,720,104,187,30,236,108,
%T A214122 1931,200,495,56,622,262,602,364,5029,386,1245,106,1624,618,1537,898,
%U A214122 12996,744,3061,206,4080,1502,3938,2186,3744,2196,33512,1422,7615,398
%N A214122 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths ending at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 4, n >= 2.
%C A214122 The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 2 to capture all geometrically distinct counts. The quarter-rectangle is read by rows. The irregular array of numbers is:
%C A214122 ....k.....1.....2.....3.....4.....5.....6.....7.....8.....9....10
%C A214122 ..n
%C A214122 ..2......10.....0
%C A214122 ..3......33.....6.....4.....0
%C A214122 ..4......90....22....22.....4
%C A214122 ..5.....256....52....67....14....88....32
%C A214122 ..6.....720...104...187....30...236...108
%C A214122 ..7....1931...200...495....56...622...262...602...364
%C A214122 ..8....5029...386..1245...106..1624...618..1537...898
%C A214122 ..9...12996...744..3061...206..4080..1502..3938..2186..3744..2196
%C A214122 .10...33512..1422..7615...398.10014..3676..9775..5466..9177..5246
%C A214122 where k indicates the position of the end node in the quarter-rectangle. For each n, the maximum value of k is 2*floor((n+1)/2). Reading this array by rows gives the sequence.
%H A214122 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 A214122 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 A214122 When n = 2, the number of times (NT) each node in the rectangle is the end node (EN) of a complete non-self-adjacent simple path is
%e A214122 EN  0  1  2  3
%e A214122     4  5  6  7
%e A214122 NT 10  0  0 10
%e A214122    10  0  0 10
%e A214122 To limit duplication, only the top left-hand corner 10 and the 0 to its right are stored in the sequence, i.e. T(2,1) = 10 and T(2,2) = 0.
%Y A214122 Cf. A213106, A213249, A213342, A214022, A214119, A214121.
%K A214122 nonn,tabf
%O A214122 2,1
%A A214122 _Christopher Hunt Gribble_, Jul 04 2012
%E A214122 Comment corrected by _Christopher Hunt Gribble_, Jul 22 2012