cp's OEIS Frontend

A214399 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 2, n >= 2.

%I A214399 #9 Jul 19 2012 14:01:30
%S A214399 6,12,14,23,24,40,42,40,68,70,70,113,116,116,122,186,190,192,202,304,
%T A214399 310,314,334,334,495,504,512,546,552,804,818,832,890,902,912,1304,
%U A214399 1326,1350,1446,1470,1490,2113,2148,2188,2346,2388,2428,2434,3422,3478,3544,3802,3874,3944,3966
%N A214399 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 2, n >= 2.
%C A214399 The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 1 to capture all geometrically distinct counts.
%C A214399 The quarter-rectangle is read by rows.
%C A214399 The irregular array of numbers is:
%C A214399 ....k....1....2....3....4....5....6....7....8....9...10
%C A214399 ..n
%C A214399 ..2......6
%C A214399 ..3.....12...14
%C A214399 ..4.....23...24
%C A214399 ..5.....40...42...40
%C A214399 ..6.....68...70...70
%C A214399 ..7....113..116..116..122
%C A214399 ..8....186..190..192..202
%C A214399 ..9....304..310..314..334..334
%C A214399 .10....495..504..512..546..552
%C A214399 .11....804..818..832..890..902..912
%C A214399 .12...1304.1326.1350.1446.1470.1490
%C A214399 .13...2113.2148.2188.2346.2388.2428.2434
%C A214399 .14...3422.3478.3544.3802.3874.3944.3966
%C A214399 .15...5540.5630.5738.6158.6278.6398.6442.6462
%C A214399 where k indicates the position of a node in the quarter-rectangle.
%C A214399 For each n, the maximum value of k is floor((n+1)/2).
%C A214399 Reading this array by rows gives the sequence.
%H A214399 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 A214399 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 A214399 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 A214399 N  0 1
%e A214399    2 3
%e A214399 NT 6 6
%e A214399    6 6
%e A214399 To limit duplication, only the top left-hand corner 6 is stored in the sequence, i.e. T(2,1) = 6.
%Y A214399 Cf. A213106, A213249, A213274, A213478, A214119, A214397.
%K A214399 nonn,tabf
%O A214399 2,1
%A A214399 _Christopher Hunt Gribble_, Jul 15 2012
%E A214399 Corrected by _Christopher Hunt Gribble_, Jul 19 2012