A316822 - OEIS

%I #6 Jun 26 2022 19:51:52

%S 1,2,2,4,8,4,8,30,30,8,16,112,169,112,16,32,420,983,983,420,32,64,

%T 1576,5701,9233,5701,1576,64,128,5912,33046,87009,87009,33046,5912,

%U 128,256,22176,191692,811854,1363249,811854,191692,22176,256,512,83184,1111756

%N T(n,k) = Number of n X k 0..1 arrays with every element unequal to 0, 1, 2, 3, 4, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ...1.....2.......4.........8..........16............32..............64

%C ...2.....8......30.......112.........420..........1576............5912

%C ...4....30.....169.......983........5701.........33046..........191692

%C ...8...112.....983......9233.......87009........811854.........7609680

%C ..16...420....5701.....87009.....1363249......20825877.......321003969

%C ..32..1576...33046....811854....20825877.....513913591.....12835573991

%C ..64..5912..191692...7609680...321003969...12835573991....521608116975

%C .128.22176.1111756..71307863..4949107992..320914969638..21245308955509

%C .256.83184.6447926.667818686.76181954073.8003158157235.862069068522225

%H R. H. Hardin, <a href="/A316822/b316822.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1);

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

%F k=3: [order 11] for n>12;

%F k=4: [order 38] for n>39.

%e Some solutions for n=5, k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A281949.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Jul 14 2018