|
%I #4 Feb 25 2017 17:49:06
%S 0,0,0,0,0,0,1,5,5,1,2,17,38,17,2,5,75,309,309,75,5,13,295,2012,3635,
%T 2012,295,13,29,1062,12160,35870,35870,12160,1062,29,65,3811,70722,
%U 346172,577003,346172,70722,3811,65,143,13107,395223,3128641,8716978
%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements.
%C Table starts
%C ...0.....0........0..........1............2..............5...............13
%C ...0.....0........5.........17...........75............295.............1062
%C ...0.....5.......38........309.........2012..........12160............70722
%C ...1....17......309.......3635........35870.........346172..........3128641
%C ...2....75.....2012......35870.......577003........8716978........124683166
%C ...5...295....12160.....346172......8716978......206993155.......4646063540
%C ..13..1062....70722....3128641....124683166.....4646063540.....163712015523
%C ..29..3811...395223...27439857...1722329260...100644923252....5565122952951
%C ..65.13107..2150350..234322382..23131988665..2119718238840..183787303136570
%C .143.44498.11454117.1959091067.303943320975.43654941219187.5933174659006889
%H R. H. Hardin, <a href="/A282969/b282969.txt">Table of n, a(n) for n = 1..220</a>
%F Empirical for column k:
%F k=1: a(n) = 3*a(n-1) -2*a(n-3) -6*a(n-4) +4*a(n-6) +6*a(n-7) +3*a(n-8) +a(n-9)
%F k=2: [order 15]
%F k=3: [order 33]
%F k=4: [order 63]
%e Some solutions for n=4 k=4
%e ..0..0..1..0. .0..0..1..1. .0..0..1..0. .0..0..0..1. .1..0..1..0
%e ..0..1..0..0. .1..0..0..0. .0..0..0..1. .1..1..1..0. .1..1..0..0
%e ..1..0..1..0. .0..0..0..0. .1..1..1..0. .0..0..0..0. .0..0..0..0
%e ..1..0..1..0. .1..1..1..1. .0..0..1..0. .1..0..1..1. .1..1..0..0
%Y Column 1 is A282831.
%K nonn,tabl
%O 1,8
%A _R. H. Hardin_, Feb 25 2017
| 