A296588 - OEIS

%I #4 Dec 16 2017 07:08:48

%S 2,3,3,5,9,5,8,22,22,8,13,62,83,62,13,21,172,346,346,172,21,34,480,

%T 1465,2458,1465,480,34,55,1358,6241,17503,17503,6241,1358,55,89,3849,

%U 26895,125765,214830,125765,26895,3849,89,144,10951,116541,923475,2607478

%N T(n,k)=Number of nXk 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0, 2 or 3 neighboring 1s.

%C Table starts

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

%C ..3.....9.....22.......62........172..........480...........1358

%C ..5....22.....83......346.......1465.........6241..........26895

%C ..8....62....346.....2458......17503.......125765.........923475

%C .13...172...1465....17503.....214830......2607478.......32689069

%C .21...480...6241...125765....2607478.....52756072.....1109882746

%C .34..1358..26895...923475...32689069...1109882746....39585589653

%C .55..3849.116541..6803610..410639937..23359296497..1408384872667

%C .89.10951.507102.50377421.5176790260.492457987101.50119033383361

%H R. H. Hardin, <a href="/A296588/b296588.txt">Table of n, a(n) for n = 1..264</a>

%F Empirical for column k:

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

%F k=2: a(n) = 3*a(n-1) +a(n-2) -a(n-3) -8*a(n-4) -3*a(n-6) -2*a(n-7) -5*a(n-8) +a(n-9)

%F k=3: [order 21]

%F k=4: [order 57]

%e Some solutions for n=4 k=4

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Dec 16 2017