A318082 - OEIS

%I #4 Aug 15 2018 13:28:17

%S 1,2,2,3,3,3,5,4,4,5,8,7,5,7,8,13,11,11,11,11,13,21,18,18,22,18,18,21,

%T 34,30,32,34,34,32,30,34,55,49,54,64,51,64,54,49,55,89,81,98,132,126,

%U 126,132,98,81,89,144,134,173,280,272,314,272,280,173,134,144,233,221,315

%N T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ..1..2...3...5....8...13....21....34.....55.....89.....144.....233......377

%C ..2..3...4...7...11...18....30....49.....81....134.....221.....365......603

%C ..3..4...5..11...18...32....54....98....173....315.....559....1008.....1813

%C ..5..7..11..22...34...64...132...280....556...1083....2208....4480.....9083

%C ..8.11..18..34...51..126...272...616...1347...2910....6602...15218....34152

%C .13.18..32..64..126..314...699..1778...4262..10254...25322...63395...158636

%C .21.30..54.132..272..699..1851..5189..13410..35181...97580..275205...756872

%C .34.49..98.280..616.1778..5189.15876..44305.131008..401009.1258378..3868741

%C .55.81.173.556.1347.4262.13410.44305.139346.466676.1583947.5508419.18965058

%H R. H. Hardin, <a href="/A318082/b318082.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1) +a(n-2)

%F k=2: a(n) = a(n-1) +2*a(n-3) -a(n-6)

%F k=3: [order 24]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+1).

%Y Column 2 is A317767.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Aug 15 2018