A283543 - OEIS

%I #4 Mar 10 2017 09:31:11

%S 2,4,4,7,11,8,13,27,33,16,24,76,127,98,32,44,201,578,573,291,64,81,

%T 537,2369,4089,2615,865,128,149,1444,10069,25532,29558,11903,2570,256,

%U 274,3859,42664,167920,282773,212441,54211,7637,512,504,10339,179733,1094959

%N T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors.

%C Table starts

%C ....2.....4.......7........13..........24............44..............81

%C ....4....11......27........76.........201...........537............1444

%C ....8....33.....127.......578........2369.........10069...........42664

%C ...16....98.....573......4089.......25532........167920.........1094959

%C ...32...291....2615.....29558......282773.......2905717........29377334

%C ...64...865...11903....212441.....3109801......49760703.......778500603

%C ..128..2570...54211...1529463....34266804.....854841910.....20707472573

%C ..256..7637..246869..11006233...377393657...14672363665....550220030803

%C ..512.22693.1124239..79212552..4156954825..251901309671..14624495679716

%C .1024.67432.5119755.570077446.45786939720.4324419947902.388675661283840

%H R. H. Hardin, <a href="/A283543/b283543.txt">Table of n, a(n) for n = 1..313</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 5*a(n-1) -a(n-2) -7*a(n-3) +10*a(n-4) +4*a(n-5) -8*a(n-6)

%F k=4: [order 8]

%F k=5: [order 21]

%F k=6: [order 27]

%F k=7: [order 59]

%F Empirical for row n:

%F n=1: a(n) = a(n-1) +a(n-2) +a(n-3)

%F n=2: a(n) = a(n-1) +3*a(n-2) +4*a(n-3)

%F n=3: a(n) = 2*a(n-1) +7*a(n-2) +11*a(n-3) -6*a(n-4) +11*a(n-5) -2*a(n-6)

%F n=4: [order 8]

%F n=5: [order 21]

%F n=6: [order 32]

%F n=7: [order 69]

%e Some solutions for n=4 k=4

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

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

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

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

%Y Column 1 is A000079.

%Y Column 2 is A282990.

%Y Row 1 is A000073(n+3).

%Y Row 2 is A282641.

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Mar 10 2017