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A300372 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%I A300372 #6 Mar 12 2018 14:28:26
%S A300372 0,0,0,0,1,0,0,1,1,0,0,1,0,1,0,0,3,3,3,3,0,0,2,3,3,3,2,0,0,6,8,4,4,8,
%T A300372 6,0,0,6,16,22,32,22,16,6,0,0,11,32,39,92,92,39,32,11,0,0,16,70,102,
%U A300372 270,366,270,102,70,16,0,0,22,135,298,1262,1592,1592,1262,298,135,22,0,0,37,293
%N A300372 T(n,k)=Number of nXk 0..1 arrays with every element equal to 2 or 3 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.
%C A300372 Table starts
%C A300372 .0..0..0...0....0.....0......0.......0........0.........0...........0
%C A300372 .0..1..1...1....3.....2......6.......6.......11........16..........22
%C A300372 .0..1..0...3....3.....8.....16......32.......70.......135.........293
%C A300372 .0..1..3...3....4....22.....39.....102......298.......833........2105
%C A300372 .0..3..3...4...32....92....270....1262.....3561.....13976.......48859
%C A300372 .0..2..8..22...92...366...1592....6925....36101....161645......762469
%C A300372 .0..6.16..39..270..1592..12042...75739...490425...3084820....19634393
%C A300372 .0..6.32.102.1262..6925..75739..729062..5841423..53750463...469053654
%C A300372 .0.11.70.298.3561.36101.490425.5841423.70536528.833035233.10021999204
%H A300372 R. H. Hardin, <a href="/A300372/b300372.txt">Table of n, a(n) for n = 1..263</a>
%F A300372 Empirical for column k:
%F A300372 k=1: a(n) = a(n-1)
%F A300372 k=2: a(n) = 2*a(n-2) +a(n-3) -a(n-4)
%F A300372 k=3: [order 14]
%F A300372 k=4: [order 43] for n>45
%e A300372 All solutions for n=5 k=4
%e A300372 ..0..0..0..0. .0..0..1..1. .0..0..1..1. .0..0..1..1
%e A300372 ..0..1..0..0. .0..1..1..0. .0..1..0..1. .0..0..1..0
%e A300372 ..1..1..1..1. .0..0..0..0. .1..0..0..1. .1..1..0..0
%e A300372 ..0..0..1..0. .0..1..1..0. .1..0..1..0. .1..0..1..1
%e A300372 ..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..1..1
%Y A300372 Column 2 is A062200(n-2).
%K A300372 nonn,tabl
%O A300372 1,17
%A A300372 _R. H. Hardin_, Mar 04 2018