A302965 - OEIS

%I #4 Apr 16 2018 11:55:29

%S 1,2,2,4,8,4,8,29,32,8,16,105,154,128,16,32,384,786,833,512,32,64,

%T 1405,3924,6206,4527,2048,64,128,5135,19868,43588,49521,24602,8192,

%U 128,256,18766,100161,314989,493132,395493,133757,32768,256,512,68589,505908

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 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.....154.......786.......3924........19868.........100161

%C ...8....128.....833......6206......43588.......314989........2257439

%C ..16....512....4527.....49521.....493132......5122000.......52646395

%C ..32...2048...24602....395493....5602382.....83644490.....1233435694

%C ..64...8192..133757...3157171...63612987...1365216668....28906043997

%C .128..32768..727293..25208524..722646394..22301032112...677939939546

%C .256.131072.3954552.201291251.8212135689.364489574945.15913688413086

%H R. H. Hardin, <a href="/A302965/b302965.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) = 7*a(n-1) -7*a(n-2) -56*a(n-4) +64*a(n-5) for n>6

%F k=4: [order 19] for n>20

%F k=5: [order 80] for n>81

%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 12] for n>13

%F n=4: [order 44] for n>45

%e Some solutions for n=5 k=4

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

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

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

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

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

%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 16 2018