A297802 T(n,k) = Number of n X k 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 5 neighboring 1's.
1, 1, 1, 1, 2, 1, 1, 11, 4, 1, 1, 24, 37, 7, 1, 1, 38, 100, 108, 14, 1, 1, 105, 293, 422, 533, 31, 1, 1, 381, 1320, 2195, 2936, 2434, 69, 1, 1, 1067, 6215, 16006, 23781, 17899, 10287, 155, 1, 1, 2676, 24879, 115773, 320168, 231921, 104985, 45968, 354, 1, 1, 7533, 99567
Offset: 1
Examples
Some solutions for n=5, k=4 ..0..1..1..1. .0..0..0..0. .0..1..1..1. .0..1..0..0. .0..1..1..0 ..0..1..1..0. .0..1..1..1. .0..0..1..1. .1..1..1..0. .0..1..1..1 ..0..0..1..0. .0..0..1..1. .1..1..0..1. .0..0..0..1. .0..1..1..1 ..1..1..0..0. .0..1..1..1. .0..1..1..1. .0..1..1..0. .1..1..0..0 ..1..1..0..0. .0..0..1..0. .0..1..1..0. .1..1..0..0. .0..0..0..0
Links
- R. H. Hardin, Table of n, a(n) for n = 1..180
Formula
Empirical for column k:
k=1: a(n) = a(n-1),
k=2: a(n) = 3*a(n-1) -2*a(n-2) +2*a(n-3) -2*a(n-4) -a(n-5),
k=3: [order 15],
k=4: [order 37],
k=5: [order 95].
Empirical for row n:
n=1: a(n) = a(n-1),
n=2: a(n) = 3*a(n-1) -2*a(n-2) +5*a(n-3) +6*a(n-4) -16*a(n-5) -12*a(n-6),
n=3: [order 21],
n=4: [order 55].
Comments