A298902 - OEIS

A298902

T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.

%I #4 Jan 28 2018 09:21:19

%S 0,0,0,0,1,0,0,1,1,0,0,2,1,2,0,0,3,2,2,3,0,0,5,3,4,3,5,0,0,8,7,10,10,

%T 7,8,0,0,13,12,24,32,24,12,13,0,0,21,25,56,120,120,56,25,21,0,0,34,47,

%U 142,471,963,471,142,47,34,0,0,55,96,346,2070,4689,4689,2070,346,96,55,0,0

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 3, 4, 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

%C .0..1..1...2....3......5.......8........13.........21...........34

%C .0..1..1...2....3......7......12........25.........47...........96

%C .0..2..2...4...10.....24......56.......142........346..........874

%C .0..3..3..10...32....120.....471......2070.......9055........39809

%C .0..5..7..24..120....963....4689.....34739.....206363......1388386

%C .0..8.12..56..471...4689...44186....522001....5379458.....62969638

%C .0.13.25.142.2070..34739..522001...9994726..165198014...3059725754

%C .0.21.47.346.9055.206363.5379458.165198014.4485120457.138682695325

%H R. H. Hardin, <a href="/A298902/b298902.txt">Table of n, a(n) for n = 1..220</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) = 2*a(n-1) +a(n-2) -2*a(n-3) +a(n-4) -2*a(n-5)

%F k=4: [order 16]

%F k=5: [order 61]

%e Some solutions for n=5 k=4

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

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

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

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

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Jan 28 2018