cp's OEIS Frontend

A214038 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.

%I A214038 #11 Jul 03 2012 15:54:59
%S A214038 34,23,16,13,347,225,142,109,298,146,74,46,2347,1842,1526,1387,2008,
%T A214038 1001,663,669,19287,16735,15113,13878,6131,9444,7697,8612,15246,6758,
%U A214038 5858,8496,163666,141849,126129,112049,132636,81112,65551,67006,118724,58677,60918,87046
%N A214038 Irregular array T(n,k) of the numbers of non-extendable (complete) non-self-adjacent simple paths starting at each of a minimal subset of nodes within a square lattice bounded by rectangles with nodal dimensions n and 8, n >= 2.
%C A214038 The subset of nodes is contained in the top left-hand quarter of the rectangle and has nodal dimensions floor((n+1)/2) and 4 to capture all geometrically distinct counts.
%C A214038 The quarter-rectangle is read by rows.
%C A214038 The irregular array of numbers is:
%C A214038 ...k......1......2......3......4......5......6......7......8......9.....10.....11.....12
%C A214038 .n
%C A214038 .2.......34.....23.....16.....13
%C A214038 .3......347....225....142....109....298....146.....74.....46
%C A214038 .4.....2347...1842...1526...1387...2008...1001....663....669
%C A214038 .5....19287..16735..15113..13878...6131...9444...7697...8612..15246...6758...5858...8496
%C A214038 .6...163666.141849.126129.112049.132636..81112..65551..67006.118724..58677..60918..87046
%C A214038 where k indicates the position of the start node in the quarter-rectangle.
%C A214038 For each n, the maximum value of k is 4*floor((n+1)/2).
%C A214038 Reading this array by rows gives the sequence.
%H A214038 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 A214038 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 A214038 When n = 2, the number of times (NT) each node in the rectangle is the start node (SN) of a complete non-self-adjacent simple path is
%e A214038 SN  0  1  2  3  4  5  6  7
%e A214038     8  9 10 11 12 13 14 15
%e A214038 NT 34 23 16 13 13 16 23 34
%e A214038    34 23 16 13 13 16 23 34
%e A214038 To limit duplication, only the top left-hand corner 34 and the 23, 16 and 13 to its right are stored in the sequence, i.e. T(2,1) = 34, T(2,2) = 23, T(2,3) = 16 and T(2,4) = 13.
%Y A214038 Cf. A213106, A213249, A213425, A213478, A213954, A214022, A214023, A214025, A214037
%K A214038 nonn,tabf
%O A214038 2,1
%A A214038 _Christopher Hunt Gribble_, Jul 01 2012