A298183 - OEIS

A298183

T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%I #4 Jan 14 2018 09:31:01

%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,3,2,2,3,0,0,5,3,3,3,5,0,0,8,5,6,6,5,

%T 8,0,0,13,8,10,15,10,8,13,0,0,21,13,15,27,27,15,13,21,0,0,34,21,26,54,

%U 53,54,26,21,34,0,0,55,34,44,117,114,114,117,44,34,55,0,0,89,55,71,237,257,231

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%C Table starts

%C .0..0..0..0...0...0....0....0.....0.....0......0......0.......0.......0

%C .0..1..1..2...3...5....8...13....21....34.....55.....89.....144.....233

%C .0..2..2..3...6..10...15...26....44....71....118....198.....327.....542

%C .0..3..3..6..15..27...54..117...237...508...1073...2261....4852...10375

%C .0..5..5.10..27..53..114..257...561..1286...2875...6483...14836...33739

%C .0..8..8.15..54.114..231..596..1462..3349...7894..19344...46083..109006

%C .0.13.13.26.117.257..596.1948..5234.14357..42469.120978..350142.1034253

%C .0.21.21.44.237.561.1462.5234.15321.48029.155245.482763.1571932.5102212

%H R. H. Hardin, <a href="/A298183/b298183.txt">Table of n, a(n) for n = 1..420</a>

%F Empirical for column k:

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

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

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

%F k=4: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4) -2*a(n-5)

%F k=5: [order 10]

%F k=6: [order 22]

%F k=7: [order 48]

%e Some solutions for n=7 k=4

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

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

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

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

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

%Y Column 2 is A000045(n-1).

%Y Column 3 is A000045(n-1).

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Jan 14 2018