A295051 - OEIS

%I #6 Nov 03 2022 21:51:55

%S 2,3,3,5,8,5,8,19,19,8,13,48,72,48,13,21,120,270,270,120,21,34,299,

%T 1027,1569,1027,299,34,55,747,3879,9045,9045,3879,747,55,89,1865,

%U 14691,52199,79855,52199,14691,1865,89,144,4656,55589,301306,700972,700972,301306

%N T(n,k) = Number of n X k 0..1 arrays with each 1 horizontally or vertically adjacent to 0 or 2 1's.

%C Table starts

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

%C ..3....8.....19.......48.......120.........299...........747...........1865

%C ..5...19.....72......270......1027........3879.........14691..........55589

%C ..8...48....270.....1569......9045.......52199........301306........1739181

%C .13..120...1027.....9045.....79855......700972.......6171389.......54282231

%C .21..299...3879....52199....700972.....9388654.....125887202.....1687776548

%C .34..747..14691...301306...6171389...125887202....2573527520....52573942625

%C .55.1865..55589..1739181..54282231..1687776548...52573942625..1637027372706

%C .89.4656.210418.10038808.477606439.22627774940.1074298644657.50976777525816

%H R. H. Hardin, <a href="/A295051/b295051.txt">Table of n, a(n) for n = 1..312</a>

%F Empirical for column k:

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

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

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

%F k=4: [order 18].

%F k=5: [order 49].

%e Some solutions for n=5, k=4

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

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Nov 13 2017