A295213 - OEIS

%I #4 Nov 17 2017 07:26:27

%S 1,1,1,1,2,1,1,4,4,1,1,7,10,7,1,1,14,27,27,14,1,1,31,102,147,102,31,1,

%T 1,69,345,916,916,345,69,1,1,155,1162,4938,9536,4938,1162,155,1,1,354,

%U 4072,27208,85215,85215,27208,4072,354,1,1,814,14224,152236,775547,1245294

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 3 1s.

%C Table starts

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

%C .1...2.....4......7.......14.........31...........69............155

%C .1...4....10.....27......102........345.........1162...........4072

%C .1...7....27....147......916.......4938........27208.........152236

%C .1..14...102....916.....9536......85215.......775547........7213161

%C .1..31...345...4938....85215....1245294.....18444470......278238087

%C .1..69..1162..27208...775547...18444470....444447937....10896495280

%C .1.155..4072.152236..7213161..278238087..10896495280...436106162865

%C .1.354.14224.848992.66719868.4170628296.265837272259.17352456088907

%H R. H. Hardin, <a href="/A295213/b295213.txt">Table of n, a(n) for n = 1..264</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 12]

%F k=4: [order 28]

%F k=5: [order 78]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A202973.

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Nov 17 2017