A305360 - OEIS

%I #4 May 31 2018 09:07:19

%S 1,1,1,1,4,1,1,7,7,1,1,13,13,13,1,1,26,21,21,26,1,1,49,27,26,27,49,1,

%T 1,99,53,64,64,53,99,1,1,194,99,115,137,115,99,194,1,1,387,197,211,

%U 271,271,211,197,387,1,1,773,371,439,656,538,656,439,371,773,1,1,1538,713,870

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

%C .1...4...7..13...26...49....99...194....387.....773....1538.....3081.....6147

%C .1...7..13..21...27...53....99...197....371.....713....1365.....2645.....5105

%C .1..13..21..26...64..115...211...439....870....1725....3513.....7141....14372

%C .1..26..27..64..137..271...656..1414...3251....7823...17334....40796....93604

%C .1..49..53.115..271..538..1476..3001...8018...19631...49142...121150...301994

%C .1..99..99.211..656.1476..4429.11281..31062...84750..233266...652271..1795948

%C .1.194.197.439.1414.3001.11281.33136..96562..302341..927289..2823816..8720038

%C .1.387.371.870.3251.8018.31062.96562.321576.1100993.3656995.12269156.41412932

%H R. H. Hardin, <a href="/A305360/b305360.txt">Table of n, a(n) for n = 1..264</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 16] for n>17

%F k=4: [order 67] for n>70

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A304004.

%Y Column 3 is A304005.

%Y Column 4 is A304006.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, May 31 2018