A303084 - OEIS

%I #4 Apr 18 2018 12:21:10

%S 1,1,2,1,2,4,1,12,2,8,1,20,32,3,16,1,72,29,112,6,32,1,168,258,90,416,

%T 10,64,1,496,432,1455,304,1512,21,128,1,1296,2525,3667,11767,1054,

%U 5472,42,256,1,3616,6313,33152,34430,84474,4182,19904,86,512,1,9760,30188,157838

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

%C Table starts

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

%C ...2..2....12....20.......72.......168..........496..........1296

%C ...4..2....32....29......258.......432.........2525..........6313

%C ...8..3...112....90.....1455......3667........33152........157838

%C ..16..6...416...304....11767.....34430.......636070.......4585419

%C ..32.10..1512..1054....84474....409478.....13375327.....170974652

%C ..64.21..5472..4182...615471...4862916....266882021....5924274499

%C .128.42.19904.17369..4647197..60442630...5754725245..218955384065

%C .256.86.72396.75377.35089147.764631608.125608726910.8100166904419

%H R. H. Hardin, <a href="/A303084/b303084.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) = 2*a(n-1) +a(n-2) -a(n-3) -2*a(n-4) +a(n-5)

%F k=3: [order 11]

%F k=4: [order 56] for n>57

%F Empirical for row n:

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

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

%F n=3: [order 17] for n>18

%F n=4: [order 67] for n>68

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 2 is A240513(n-2).

%Y Row 2 is A302368.

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Apr 18 2018