A302808 - OEIS

%I #4 Apr 13 2018 13:09:15

%S 1,2,2,4,8,4,8,29,32,8,16,105,169,128,16,32,384,934,1010,512,32,64,

%T 1405,5117,8718,6084,2048,64,128,5135,28128,74072,82367,36456,8192,

%U 128,256,18766,154494,632004,1089773,773520,218640,32768,256,512,68589,848519

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 5 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

%C ...1......2.......4.........8..........16............32..............64

%C ...2......8......29.......105.........384..........1405............5135

%C ...4.....32.....169.......934........5117.........28128..........154494

%C ...8....128....1010......8718.......74072........632004.........5396562

%C ..16....512....6084.....82367.....1089773......14458177.......192211013

%C ..32...2048...36456....773520....15904814.....327603711......6769884156

%C ..64...8192..218640...7267160...232260380....7428713676....238687785290

%C .128..32768.1312416..68346451..3396923500..168777255305...8434497360938

%C .256.131072.7873344.642498696.49653502029.3832039683236.297820640670676

%H R. H. Hardin, <a href="/A302808/b302808.txt">Table of n, a(n) for n = 1..180</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 6*a(n-1) +24*a(n-3) -144*a(n-4) for n>6

%F k=4: [order 18] for n>20

%F k=5: [order 90] for n>92

%F Empirical for row n:

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

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

%F n=3: [order 13] for n>15

%F n=4: [order 48] for n>50

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000079(n-1).

%Y Column 2 is A004171(n-1).

%Y Row 1 is A000079(n-1).

%Y Row 2 is A302266.

%K nonn,tabl

%O 1,2

%A _R. H. Hardin_, Apr 13 2018