cp's OEIS Frontend

A214608 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 9, n >= 2.

%I A214608 #4 Jul 23 2012 12:49:15
%S A214608 304,310,314,334,334,4137,4754,4811,4929,4920,4610,5260,4738,4784,
%T A214608 4924,50775,66474,72137,71469,69764,65977,63790,55400,55907,57274,
%U A214608 676474,969677,1118226,1096104,1058044,1003962,946620,864012,870946,884912,1154902,887242,651592,669896,710904
%N A214608 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 9, n >= 2.
%C A214608 The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 5 to capture all geometrically distinct counts.
%C A214608 The quarter-rectangle is read by rows.
%C A214608 The irregular array of numbers is:
%C A214608 ...k......1.......2.......3.......4.......5.......6.......7.......8.......9......10......11......12......13......14......15
%C A214608 .n
%C A214608 .2......304.....310.....314.....334.....334
%C A214608 .3.....4137....4754....4811....4929....4920....4610....5260....4738....4784....4924
%C A214608 .4....50775...66474...72137...71469...69764...65977...63790...55400...55907...57274
%C A214608 .5...676474..969677.1118226.1096104.1058044.1003962..946620..864012..870946..884912.1154902..887242..651592..669896..710904
%C A214608 where k indicates the position of a node in the quarter-rectangle.
%C A214608 For each n, the maximum value of k is 5*floor((n+1)/2).
%C A214608 Reading this array by rows gives the sequence.
%H A214608 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 A214608 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 A214608 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 A214608 N    0   1   2   3   4   5   6   7   8
%e A214608      9  10  11  12  13  14  15  16  17
%e A214608 NT 304 310 314 334 334 334 314 310 304
%e A214608    304 310 314 334 334 334 314 310 304
%e A214608 To limit duplication, only the top left-hand corner 304 and the 310, 314, 334, 334 to its right are stored in the sequence,
%e A214608 i.e. T(2,1) = 304, T(2,2) = 310, T(2,3) = 314, T(2,4) = 334 and T(2,5) = 334.
%Y A214608 Cf. A213106, A213249, A213426, A214042, A214376, A214397, A214399, A214504, A214510, A214563, A214601, A214503, A214605
%K A214608 nonn,tabf
%O A214608 2,1
%A A214608 _Christopher Hunt Gribble_, Jul 22 2012