A297802 - OEIS

%I #6 Apr 17 2022 22:18:20

%S 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,

%T 31,1,1,381,1320,2195,2936,2434,69,1,1,1067,6215,16006,23781,17899,

%U 10287,155,1,1,2676,24879,115773,320168,231921,104985,45968,354,1,1,7533,99567

%N 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.

%C Table starts

%C .1...1......1.......1.........1...........1.............1...............1

%C .1...2.....11......24........38.........105...........381............1067

%C .1...4.....37.....100.......293........1320..........6215...........24879

%C .1...7....108.....422......2195.......16006........115773..........738989

%C .1..14....533....2936.....23781......320168.......4340367........46828204

%C .1..31...2434...17899....231921.....5511367.....123361724......2122878239

%C .1..69..10287..104985...2174696....91376524....3420197908.....94927605755

%C .1.155..45968..645568..21427001..1587468720..102189481612...4611250894511

%C .1.354.207906.3978117.209042911.27421636815.2993486726263.218072722004943

%H R. H. Hardin, <a href="/A297802/b297802.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

%F k=1: a(n) = 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),

%F k=3: [order 15],

%F k=4: [order 37],

%F k=5: [order 95].

%F Empirical for row n:

%F n=1: a(n) = a(n-1),

%F 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),

%F n=3: [order 21],

%F n=4: [order 55].

%e Some solutions for n=5, k=4

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

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

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

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

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

%Y Column 2 is A202973.

%Y Row 2 is A297545.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 06 2018