|
%I #6 Sep 03 2022 21:13:12
%S 2,4,4,8,16,8,16,49,57,16,32,161,264,209,32,64,548,1521,1525,768,64,
%T 128,1824,8687,15226,8732,2816,128,256,6081,47829,149840,150497,49924,
%U 10329,256,512,20353,268285,1392868,2530461,1489917,285770,37889,512,1024
%N T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors.
%C Table starts
%C ...2......4.......8.........16...........32.............64..............128
%C ...4.....16......49........161..........548...........1824.............6081
%C ...8.....57.....264.......1521.........8687..........47829...........268285
%C ..16....209....1525......15226.......149840........1392868.........13354587
%C ..32....768....8732.....150497......2530461.......39372084........640543058
%C ..64...2816...49924....1489917.....42865601.....1119189256......30968693109
%C .128..10329..285770...14754038....726353972....31815868749....1496646288297
%C .256..37889.1635402..146079023..12304063774...904083654190...72299799564414
%C .512.138980.9359104.1446386879.208447516852.25694926726796.3493423029563345
%H R. H. Hardin, <a href="/A283691/b283691.txt">Table of n, a(n) for n = 1..264</a>
%F Empirical for column k:
%F k=1: a(n) = 2*a(n-1).
%F k=2: a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5).
%F k=3: [order 10].
%F k=4: [order 14].
%F k=5: [order 40].
%F k=6: [order 83].
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1).
%F n=2: a(n) = 3*a(n-1) +a(n-2) +3*a(n-3) -6*a(n-4) -8*a(n-5).
%F n=3: [order 11].
%F n=4: [order 23].
%F n=5: [order 56].
%e Some solutions for n=4, k=4
%e ..1..0..1..1. .1..0..0..0. .0..0..1..0. .0..0..0..1. .1..0..1..0
%e ..0..0..0..0. .1..0..1..0. .0..0..0..1. .0..0..0..0. .1..0..0..0
%e ..1..1..0..1. .0..1..0..0. .0..0..0..1. .0..1..1..0. .0..0..0..1
%e ..1..0..0..1. .0..1..0..1. .1..0..0..1. .1..0..0..0. .0..0..0..1
%Y Column 1 is A000079.
%Y Column 2 is A283124.
%Y Row 1 is A000079.
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Mar 14 2017
| 