|
%I #4 Jul 07 2018 08:27:52
%S 1,1,1,1,4,1,1,8,8,1,1,24,11,24,1,1,82,40,40,82,1,1,272,94,246,94,272,
%T 1,1,908,291,899,899,291,908,1,1,3076,776,4262,3180,4262,776,3076,1,1,
%U 10444,2269,18773,17695,17695,18773,2269,10444,1,1,35480,6275,86217
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 4, 7 or 8 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1.....1....1......1.......1........1.........1..........1............1
%C .1.....4....8.....24......82......272.......908.......3076........10444
%C .1.....8...11.....40......94......291.......776.......2269.........6275
%C .1....24...40....246.....899.....4262.....18773......86217.......393045
%C .1....82...94....899....3180....17695.....88597.....457091......2402617
%C .1...272..291...4262...17695...129257....873130....5763068.....41285414
%C .1...908..776..18773...88597...873130...8469438...69549901....725190299
%C .1..3076.2269..86217..457091..5763068..69549901..730909482...9689842501
%C .1.10444.6275.393045.2402617.41285414.725190299.9689842501.185758559665
%H R. H. Hardin, <a href="/A316576/b316576.txt">Table of n, a(n) for n = 1..199</a>
%F Empirical for column k:
%F k=1: a(n) = a(n-1)
%F k=2: a(n) = 4*a(n-1) -2*a(n-2) +2*a(n-3) -6*a(n-4) -4*a(n-5) for n>6
%F k=3: [order 19] for n>20
%F k=4: [order 49] for n>52
%e Some solutions for n=5 k=4
%e ..0..1..0..1. .0..1..0..0. .0..1..1..0. .0..0..1..1. .0..0..1..0
%e ..1..1..0..1. .1..1..1..1. .0..1..0..1. .1..1..0..0. .1..1..1..1
%e ..0..1..1..1. .0..0..1..1. .1..1..1..1. .1..1..0..0. .1..1..1..0
%e ..1..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..1. .0..0..0..1
%e ..1..0..0..0. .1..1..0..1. .1..1..1..0. .0..0..1..1. .0..0..0..1
%Y Column 2 is A303882.
%Y Column 3 is A304889.
%Y Column 4 is A304890.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jul 07 2018
|
