editing

approved

T(n,k) = Number of nXk n X k 0..1 arrays with each 1 horizontally or vertically adjacent to 0 or 2 1s1's.

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

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

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).

k=4: [order 18].

k=5: [order 49].

Some solutions for n=5 , k=4

approved

editing

editing

approved

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

allocated for R. H. Hardin

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

2, 3, 3, 5, 8, 5, 8, 19, 19, 8, 13, 48, 72, 48, 13, 21, 120, 270, 270, 120, 21, 34, 299, 1027, 1569, 1027, 299, 34, 55, 747, 3879, 9045, 9045, 3879, 747, 55, 89, 1865, 14691, 52199, 79855, 52199, 14691, 1865, 89, 144, 4656, 55589, 301306, 700972, 700972, 301306

1,1

Table starts

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

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

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

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

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

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

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

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

.89.4656.210418.10038808.477606439.22627774940.1074298644657.50976777525816

Empirical for column k:

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

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

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)

k=4: [order 18]

k=5: [order 49]

Some solutions for n=5 k=4

..0..0..1..0. .0..1..0..0. .0..1..1..0. .1..0..0..0. .1..0..1..0

..1..0..0..1. .1..0..1..0. .0..1..1..0. .0..0..0..0. .0..0..0..0

..0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1

..0..0..0..1. .0..0..0..0. .0..0..1..1. .0..0..0..0. .1..1..0..0

..0..1..0..0. .0..0..0..0. .1..0..1..1. .0..0..1..0. .1..1..0..0

Column 1 is A000045(n+2).

allocated

nonn,tabl

R. H. Hardin, Nov 13 2017

approved

editing

allocated for R. H. Hardin

allocated

approved