A301906 - OEIS

%I #4 Mar 28 2018 16:09:22

%S 1,1,2,1,1,4,1,2,1,8,1,2,3,1,16,1,3,2,7,1,32,1,6,2,5,16,1,64,1,10,7,8,

%T 10,43,1,128,1,21,12,40,12,26,117,1,256,1,42,27,96,92,64,65,330,1,512,

%U 1,86,62,316,320,532,196,170,935,1,1024,1,179,160,1078,1588,1934,1999,864,442

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

%C Table starts

%C ...1.1...1...1....1.....1......1.......1........1..........1...........1

%C ...2.1...2...2....3.....6.....10......21.......42.........86.........179

%C ...4.1...3...2....2.....7.....12......27.......62........160.........387

%C ...8.1...7...5....8....40.....96.....316.....1078.......3831.......13331

%C ..16.1..16..10...12....92....320....1588.....7234......34477......171770

%C ..32.1..43..26...64...532...1934...14860....86638.....568382.....4029337

%C ..64.1.117..65..196..1999...8781..104732...770376....7398173....75183520

%C .128.1.330.170..864.10150..49709..952467..8263384..113474387..1620307756

%C .256.1.935.442.3236.46226.253844.7931939.81388360.1622304450.32687652025

%H R. H. Hardin, <a href="/A301906/b301906.txt">Table of n, a(n) for n = 1..287</a>

%F Empirical for column k:

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

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

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

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

%F k=5: a(n) = 4*a(n-1) +5*a(n-2) -20*a(n-3) -4*a(n-4) +16*a(n-5) for n>6

%F k=6: [order 20] for n>21

%F k=7: [order 30] for n>33

%F Empirical for row n:

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

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

%F n=3: [order 30] for n>31

%e Some solutions for n=5 k=4

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

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

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

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

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

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

%Y Column 4 is A245306(n-1).

%Y Row 2 is A240513(n-3).

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Mar 28 2018