A299574 - OEIS

%I #4 Feb 13 2018 11:19:04

%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,25,25,23,5,8,49,47,78,47,49,8,

%T 13,99,113,237,237,113,99,13,21,189,265,844,766,844,265,189,21,34,383,

%U 621,2604,3324,3324,2604,621,383,34,55,777,1473,8136,15186,17389,15186,8136

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C ..0...1....1.....2......3.......5........8........13.........21..........34

%C ..1...3....7....13.....23......49.......99.......189........383.........777

%C ..1...7...15....25.....47.....113......265.......621.......1473........3443

%C ..2..13...25....78....237.....844.....2604......8136......26760.......86924

%C ..3..23...47...237....766....3324....15186.....56870.....234074.....1011095

%C ..5..49..113...844...3324...17389....98466....505680....2704280....14896422

%C ..8..99..265..2604..15186...98466...784334...5286269...38000347...284230090

%C .13.189..621..8136..56870..505680..5286269..46965400..449355259..4443621368

%C .21.383.1473.26760.234074.2704280.38000347.449355259.5736969146.75908899351

%H R. H. Hardin, <a href="/A299574/b299574.txt">Table of n, a(n) for n = 1..199</a>

%F Empirical for column k:

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

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

%F k=3: [order 14] for n>15

%F k=4: [order 67] for n>68

%e Some solutions for n=6 k=7

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

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

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

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

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

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

%Y Column 1 is A000045(n-1).

%Y Column 2 is A297953.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Feb 13 2018