A302224 - OEIS

%I #4 Apr 03 2018 12:16:35

%S 0,1,0,1,3,0,2,14,11,0,3,45,43,34,0,5,146,164,194,111,0,8,537,760,934,

%T 675,361,0,13,1934,3425,6110,4237,2666,1172,0,21,6861,15569,38736,

%U 40395,21777,9819,3809,0,34,24386,70323,251254,338204,292781,105585,37382

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

%C .0.....3.....14......45.......146........537........1934..........6861

%C .0....11.....43.....164.......760.......3425.......15569.........70323

%C .0....34....194.....934......6110......38736......251254.......1610569

%C .0...111....675....4237.....40395.....338204.....3018243......26373655

%C .0...361...2666...21777....292781....3420704....42508145.....524715109

%C .0..1172...9819..105585...2043848...32181643...553097760....9458629708

%C .0..3809..37382..523414..14419536..310963650..7403262824..177191137344

%C .0.12377.140039.2578424.101511446.2973099477.97939043966.3265007473096

%H R. H. Hardin, <a href="/A302224/b302224.txt">Table of n, a(n) for n = 1..181</a>

%F Empirical for column k:

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

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

%F k=3: [order 11]

%F k=4: [order 30] for n>34

%F k=5: [order 92] for n>97

%F Empirical for row n:

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

%F n=2: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) +10*a(n-4) +4*a(n-5) for n>6

%F n=3: [order 15] for n>17

%F n=4: [order 54] for n>58

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 2 is A180762.

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

%K nonn,tabl

%O 1,5

%A _R. H. Hardin_, Apr 03 2018