A297959 - OEIS

%I #4 Jan 09 2018 07:57:55

%S 0,1,1,1,3,1,2,7,7,2,3,13,15,13,3,5,23,25,25,23,5,8,49,47,78,47,49,8,

%T 13,99,109,233,233,109,99,13,21,189,245,779,681,779,245,189,21,34,383,

%U 545,2359,2596,2596,2359,545,383,34,55,777,1253,7024,11623,11283,11623,7024

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

%C Table starts

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

%C ..1...3....7....13.....23......49.......99.......189........383.........777

%C ..1...7...15....25.....47.....109......245.......545.......1253........2859

%C ..2..13...25....78....233.....779.....2359......7024......21572.......66763

%C ..3..23...47...233....681....2596....11623.....39801.....149442......616286

%C ..5..49..109...779...2596...11283....61204....284304....1375342.....6952910

%C ..8..99..245..2359..11623...61204...483929...2884282...18478260...127847471

%C .13.189..545..7024..39801..284304..2884282..22145365..186612398..1682179108

%C .21.383.1253.21572.149442.1375342.18478260.186612398.2092206702.24910286308

%H R. H. Hardin, <a href="/A297959/b297959.txt">Table of n, a(n) for n = 1..219</a>

%F Empirical for column k:

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

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

%F k=3: [order 12] for n>13

%F k=4: [order 62] for n>65

%e Some solutions for n=6 k=4

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

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

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

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

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

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

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Jan 09 2018