login
A297802
T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 5 neighboring 1's.
12
1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 37, 7, 1, 1, 38, 100, 108, 14, 1, 1, 105, 293, 422, 533, 31, 1, 1, 381, 1320, 2195, 2936, 2434, 69, 1, 1, 1067, 6215, 16006, 23781, 17899, 10287, 155, 1, 1, 2676, 24879, 115773, 320168, 231921, 104985, 45968, 354, 1, 1, 7533, 99567
OFFSET
1,5
COMMENTS
Table starts
.1...1......1.......1.........1...........1.............1...............1
.1...2.....11......24........38.........105...........381............1067
.1...4.....37.....100.......293........1320..........6215...........24879
.1...7....108.....422......2195.......16006........115773..........738989
.1..14....533....2936.....23781......320168.......4340367........46828204
.1..31...2434...17899....231921.....5511367.....123361724......2122878239
.1..69..10287..104985...2174696....91376524....3420197908.....94927605755
.1.155..45968..645568..21427001..1587468720..102189481612...4611250894511
.1.354.207906.3978117.209042911.27421636815.2993486726263.218072722004943
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1),
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5),
k=3: [order 15],
k=4: [order 37],
k=5: [order 95].
Empirical for row n:
n=1: a(n) = a(n-1),
n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6),
n=3: [order 21],
n=4: [order 55].
EXAMPLE
Some solutions for n=5, k=4
..0..1..1..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .0..1..1..0
..0..1..1..0. .0..1..1..1. .0..0..1..1. .1..1..1..0. .0..1..1..1
..0..0..1..0. .0..0..1..1. .1..1..0..1. .0..0..0..1. .0..1..1..1
..1..1..0..0. .0..1..1..1. .0..1..1..1. .0..1..1..0. .1..1..0..0
..1..1..0..0. .0..0..1..0. .0..1..1..0. .1..1..0..0. .0..0..0..0
CROSSREFS
Column 2 is A202973.
Row 2 is A297545.
Sequence in context: A110905 A205447 A297544 * A232266 A234013 A158202
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 06 2018
STATUS
approved