|
%I #4 Jun 24 2018 16:36:24
%S 1,1,1,1,4,1,1,7,7,1,1,13,13,13,1,1,26,23,23,26,1,1,49,47,56,47,49,1,
%T 1,99,144,213,213,144,99,1,1,194,391,702,1109,702,391,194,1,1,387,
%U 1118,2524,5426,5426,2524,1118,387,1,1,773,3330,9034,26626,43480,26626,9034
%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.
%C Table starts
%C .1...1....1.....1......1........1.........1..........1............1
%C .1...4....7....13.....26.......49........99........194..........387
%C .1...7...13....23.....47......144.......391.......1118.........3330
%C .1..13...23....56....213......702......2524.......9034........33185
%C .1..26...47...213...1109.....5426.....26626.....133245.......708063
%C .1..49..144...702...5426....43480....283238....2064800.....15977233
%C .1..99..391..2524..26626...283238...2525039...25192165....261795432
%C .1.194.1118..9034.133245..2064800..25192165..351431316...5223691497
%C .1.387.3330.33185.708063.15977233.261795432.5223691497.112149224917
%H R. H. Hardin, <a href="/A316123/b316123.txt">Table of n, a(n) for n = 1..197</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 17] for n>19
%F k=4: [order 70] for n>71
%e Some solutions for n=5 k=4
%e ..0..1..1..0. .0..1..1..0. .0..0..0..1. .0..1..1..0. .0..0..0..0
%e ..1..1..0..1. .1..0..1..1. .1..1..0..1. .0..1..0..1. .1..1..1..1
%e ..1..0..1..1. .1..1..1..0. .0..1..1..0. .1..0..0..1. .1..1..1..1
%e ..0..1..0..1. .0..0..1..1. .1..1..0..1. .1..1..1..0. .1..1..1..1
%e ..1..0..0..1. .1..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
%Y Column 2 is A304004.
%K nonn,tabl
%O 1,5
%A _R. H. Hardin_, Jun 24 2018
|
