A316620 - OEIS

%I #4 Jul 08 2018 16:26:53

%S 1,1,1,1,4,1,1,7,7,1,1,13,13,13,1,1,26,21,21,26,1,1,49,29,26,29,49,1,

%T 1,99,58,70,70,58,99,1,1,194,120,139,189,139,120,194,1,1,387,250,287,

%U 468,468,287,250,387,1,1,773,515,625,1446,1916,1446,625,515,773,1,1,1538

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5, 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.........1.........1

%C .1...4...7...13....26....49.....99.....194......387.......773......1538

%C .1...7..13...21....29....58....120.....250......515......1100......2302

%C .1..13..21...26....70...139....287.....625.....1484......3197......7321

%C .1..26..29...70...189...468...1446....3769....11196.....32714.....93764

%C .1..49..58..139...468..1916...5428...18126....66146....225773....773853

%C .1..99.120..287..1446..5428..20777...86855...376999...1555947...6605299

%C .1.194.250..625..3769.18126..86855..476965..2572180..13348093..71288692

%C .1.387.515.1484.11196.66146.376999.2572180.16700783.105494740.692447139

%H R. H. Hardin, <a href="/A316620/b316620.txt">Table of n, a(n) for n = 1..220</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5

%F k=3: [order 18] for n>19

%F k=4: [order 70] for n>71

%e Some solutions for n=5 k=4

%e ..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..1..0..0. .0..1..1..0

%e ..1..1..0..0. .1..1..1..1. .0..0..1..1. .1..0..1..1. .0..1..0..1

%e ..1..0..0..0. .1..0..0..1. .0..0..0..1. .0..1..1..1. .1..0..0..1

%e ..1..0..1..1. .1..0..0..1. .1..1..0..1. .1..0..1..1. .0..1..0..1

%e ..0..1..1..0. .1..0..0..1. .0..1..1..0. .0..1..0..0. .0..1..1..0

%Y Column 2 is A304004.

%Y Column 3 is A304947.

%Y Column 4 is A304948.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jul 08 2018