|
%I #14 Apr 11 2022 16:38:04
%S 2,2,4,4,10,8,7,34,21,16,12,107,153,48,32,21,342,865,776,113,64,37,
%T 1069,4665,7697,3861,261,128,65,3381,25556,70462,66499,18721,601,256,
%U 114,10689,144847,680302,1031105,571226,91993,1390,512,200,33808,817539
%N T(n,k)=Number of nXk 0..1 arrays with no element less than a strict majority of its horizontal, diagonal and antidiagonal neighbors
%C Table starts
%C ....2....2........4..........7...........12..............21................37
%C ....4...10.......34........107..........342............1069..............3381
%C ....8...21......153........865.........4665...........25556............144847
%C ...16...48......776.......7697........70462..........680302...........6935963
%C ...32..113.....3861......66499......1031105........17572772.........322599407
%C ...64..261....18721.....571226.....15000701.......451200772.......14940780666
%C ..128..601....91993....4944075....219937967.....11683058939......697702378939
%C ..256.1390...453274...42759650...3222629836....302190345444....32529760276112
%C ..512.3216..2223662..369356733..47159743290...7806399525348..1514885617016157
%C .1024.7435.10915727.3191749214.690399979855.201765495180944.70592106166184098
%H R. H. Hardin, <a href="/A231523/b231523.txt">Table of n, a(n) for n = 1..220</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) -2*a(n-4) -a(n-5) for n>6
%F k=3: [order 13] for n>14
%F k=4: [order 24] for n>25
%F k=5: [order 70] for n>71
%F Empirical for row n:
%F n=1: a(n) = 2*a(n-1) -a(n-2) +a(n-3) for n>4
%F n=2: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)
%F n=3: [order 16] for n>17
%F n=4: [order 39] for n>40
%e Some solutions for n=4 k=4
%e ..1..0..0..0....1..0..1..1....1..1..0..1....0..0..0..0....0..1..0..1
%e ..1..0..0..0....0..0..0..1....1..0..0..0....0..0..0..1....1..0..0..0
%e ..0..0..0..0....0..0..1..0....0..0..0..1....1..0..0..1....1..0..1..0
%e ..0..1..1..1....0..0..0..0....0..1..0..0....0..0..0..1....0..0..0..1
%Y Column 1 is A000079
%Y Column 2 is A231376
%Y Row 1 is A005251(n+2)
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Nov 10 2013
| 