A299314 - OEIS

%I #4 Feb 06 2018 13:38:54

%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,29,29,23,5,8,49,63,112,63,49,8,

%T 13,99,199,504,504,199,99,13,21,189,593,2528,3463,2528,593,189,21,34,

%U 383,1657,11252,24519,24519,11252,1657,383,34,55,777,4689,50720,167810

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

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

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

%C ..1...7...15.....29......63.......199.........593.........1657...........4689

%C ..2..13...29....112.....504......2528.......11252........50720.........241309

%C ..3..23...63....504....3463.....24519......167810......1165033........8305148

%C ..5..49..199...2528...24519....270346.....3203795.....36378590......417642077

%C ..8..99..593..11252..167810...3203795....60731972...1089584523....20249517439

%C .13.189.1657..50720.1165033..36378590..1089584523..30975700202...924197633148

%C .21.383.4689.241309.8305148.417642077.20249517439.924197633148.44405195921475

%H R. H. Hardin, <a href="/A299314/b299314.txt">Table of n, a(n) for n = 1..180</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 16] for n>17

%F k=4: [order 62] for n>66

%e Some solutions for n=5 k=4

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

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

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

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

%e ..0..1..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..0. .0..1..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 06 2018