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A302212 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero. 12

%I

%S 1,1,2,1,2,4,1,11,2,8,1,13,16,3,16,1,34,5,47,6,32,1,65,32,7,147,10,64,

%T 1,123,22,111,18,386,21,128,1,266,72,80,448,55,1065,42,256,1,499,101,

%U 424,281,1725,172,3063,86,512,1,1037,216,1157,1868,1395,6423,575,8624,179

%N T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally 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..2...11...13....34.....65.....123......266......499.......1037........2042

%C ...4..2...16....5....32.....22......72......101......216........486.........968

%C ...8..3...47....7...111.....80.....424.....1157.....2922......12816.......33744

%C ..16..6..147...18...448....281....1868.....6036....16344.....110672......332791

%C ..32.10..386...55..1725...1395...11170....46215...142804....1296927.....3754619

%C ..64.21.1065..172..6423...8756...55922...465040..1136003...19265064....60547641

%C .128.42.3063..575.24927..43128..291320..3509969..9080114..212347228...786789878

%C .256.86.8624.1962.96909.234170.1544411.29343177.73189971.2698247985.11028726211

%H R. H. Hardin, <a href="/A302212/b302212.txt">Table of n, a(n) for n = 1..240</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 9]

%F k=4: [order 28] for n>32

%F k=5: [order 37] for n>41

%F Empirical for row n:

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

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

%F n=3: [order 19] for n>20

%F n=4: [order 61] for n>62

%e Some solutions for n=5 k=4

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

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

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

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

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

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

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

%Y Row 2 is A297870(n+2).

%K nonn,tabl

%O 1,3

%A _R. H. Hardin_, Apr 03 2018

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Last modified January 27 20:46 EST 2022. Contains 350613 sequences. (Running on oeis4.)