A298589 - OEIS

%I #4 Jan 22 2018 06:53:40

%S 1,1,1,1,1,1,1,1,1,1,1,2,9,2,1,1,5,5,5,5,1,1,9,16,4,16,9,1,1,22,31,13,

%T 13,31,22,1,1,45,28,31,65,31,28,45,1,1,101,87,83,233,233,83,87,101,1,

%U 1,218,125,262,441,1112,441,262,125,218,1,1,477,185,819,1765,4620,4620,1765

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C .1...1...1...2....5......9......22.......45........101.........218..........477

%C .1...1...9...5...16.....31......28.......87........125.........185..........418

%C .1...2...5...4...13.....31......83......262........819........2690.........8887

%C .1...5..16..13...65....233.....441.....1765.......7431.......28212.......121244

%C .1...9..31..31..233...1112....4620....29589.....169601.....1004366......6170528

%C .1..22..28..83..441...4620...26343...240692....2382399....22651784....228684042

%C .1..45..87.262.1765..29589..240692..3833927...54266663...764702068..11301659452

%C .1.101.125.819.7431.169601.2382399.54266663.1239155011.27405626123.629168904793

%H R. H. Hardin, <a href="/A298589/b298589.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

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

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

%F k=3: [order 9] for n>13

%F k=4: [order 34]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A052962(n-2).

%K nonn,tabl

%O 1,12

%A _R. H. Hardin_, Jan 22 2018