login
A301669
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2 or 4 horizontally or vertically adjacent elements, with upper left element zero.
7
0, 1, 1, 1, 3, 1, 2, 10, 10, 2, 3, 23, 30, 23, 3, 5, 61, 118, 118, 61, 5, 8, 162, 407, 564, 407, 162, 8, 13, 421, 1498, 2793, 2793, 1498, 421, 13, 21, 1103, 5289, 14394, 21224, 14394, 5289, 1103, 21, 34, 2890, 19184, 71564, 146841, 146841, 71564, 19184, 2890, 34, 55
OFFSET
1,5
COMMENTS
Table starts
..0....1.....1.......2........3..........5...........8............13
..1....3....10......23.......61........162.........421..........1103
..1...10....30.....118......407.......1498........5289.........19184
..2...23...118.....564.....2793......14394.......71564........359659
..3...61...407....2793....21224.....146841.....1073621.......7703565
..5..162..1498...14394...146841....1537496....15498505.....159497778
..8..421..5289...71564..1073621...15498505...225780260....3307561389
.13.1103.19184..359659..7703565..159497778..3307561389...68862687289
.21.2890.68832.1808256.55506215.1631501428.48158543096.1434208027966
LINKS
FORMULA
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) +2*a(n-3) -a(n-4)
k=3: [order 20]
k=4: [order 70]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..1..1. .0..0..0..1. .0..1..1..1. .0..0..1..1
..0..1..0..1. .1..0..1..0. .1..1..1..1. .0..0..0..0. .1..1..0..1
..1..1..0..0. .1..0..0..0. .1..0..0..0. .1..1..1..0. .0..0..0..0
..1..0..1..1. .1..1..1..1. .0..1..1..0. .1..0..1..0. .0..1..0..1
..1..0..0..1. .0..0..0..1. .0..0..1..0. .1..0..1..0. .0..1..1..1
CROSSREFS
Column 1 is A000045(n-1).
Column 2 is A185828.
Sequence in context: A316757 A055450 A185835 * A300427 A300689 A300612
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 25 2018
STATUS
approved