%I #6 Dec 18 2015 18:17:44
%S 1,1,4,1,5,25,1,5,113,232,1,5,178,7696,3182,1,5,193,39317,1429748,
%T 65372,1,5,194,80780,35539864,723276072,1988549,1,5,194,103442,
%U 225623340,123214409287,996233663484,90079152,1,5,194,109314,625181527
%N T(n,k)=Number of lower triangles of an n X n 0..k array with new values introduced in row major order 0..k and no element equal to more than two horizontal or vertical neighbors
%C Table starts
%C ........1................1....................1.......................1
%C ........4................5....................5.......................5
%C .......25..............113..................178.....................193
%C ......232.............7696................39317...................80780
%C .....3182..........1429748.............35539864...............225623340
%C ....65372........723276072.........123214409287...........3211386454648
%C ..1988549.....996233663484.....1633861873067053......223665935176544829
%C .90079152.3736289882783364.82861549363088245839.76009506543180381646618
%H R. H. Hardin, <a href="/A194576/b194576.txt">Table of n, a(n) for n = 1..88</a>
%e Some solutions for n=4 k=3
%e ..0........0........0........0........0........0........0........0
%e ..1.2......1.2......1.2......1.2......1.1......1.2......0.1......1.0
%e ..0.1.2....1.3.3....0.3.0....2.0.0....1.0.2....2.2.0....0.2.1....0.2.0
%e ..0.0.0.0..1.3.1.1..0.3.0.3..0.3.0.3..1.3.3.2..1.1.1.3..2.1.0.0..2.2.1.0
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Aug 29 2011