A296335 - OEIS

%I #4 Dec 10 2017 12:10:19

%S 2,3,3,5,8,5,8,19,19,8,13,47,64,47,13,21,116,230,230,116,21,34,286,

%T 816,1235,816,286,34,55,705,2895,6504,6504,2895,705,55,89,1738,10277,

%U 34224,50595,34224,10277,1738,89,144,4285,36480,180404,392230,392230,180404

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0 or 2 neighboring 1s.

%C Table starts

%C ..2....3......5.......8........13.........21...........34............55

%C ..3....8.....19......47.......116........286..........705..........1738

%C ..5...19.....64.....230.......816.......2895........10277.........36480

%C ..8...47....230....1235......6504......34224.......180404........950451

%C .13..116....816....6504.....50595.....392230......3051494......23717411

%C .21..286...2895...34224....392230....4476519.....51335713.....587914968

%C .34..705..10277..180404...3051494...51335713....869077778...14686634221

%C .55.1738..36480..950451..23717411..587914968..14686634221..366077961514

%C .89.4285.129486.5007796.184355308.6733523523.248214082895.9126072558650

%H R. H. Hardin, <a href="/A296335/b296335.txt">Table of n, a(n) for n = 1..419</a>

%F Empirical for column k:

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

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

%F k=3: a(n) = 2*a(n-1) +4*a(n-2) +5*a(n-3) +2*a(n-4) -2*a(n-5) -3*a(n-6) -2*a(n-7) +a(n-9)

%F k=4: [order 21]

%F k=5: [order 44]

%e Some solutions for n=5 k=4

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

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

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

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

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

%Y Column 1 is A000045(n+2).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 10 2017