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A302728
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
10
0, 1, 0, 1, 3, 0, 2, 7, 10, 0, 3, 10, 22, 23, 0, 5, 27, 29, 83, 61, 0, 8, 45, 74, 89, 301, 162, 0, 13, 98, 162, 287, 353, 1079, 421, 0, 21, 193, 363, 689, 1307, 941, 4064, 1103, 0, 34, 379, 782, 1723, 4505, 4491, 3316, 15183, 2890, 0, 55, 778, 1766, 4491, 16265, 20842, 17828
OFFSET
1,5
COMMENTS
Table starts
.0....1.....1.....2......3.......5........8........13........21.........34
.0....3.....7....10.....27......45.......98.......193.......379........778
.0...10....22....29.....74.....162......363.......782......1766.......3953
.0...23....83....89....287.....689.....1723......4491.....10433......28009
.0...61...301...353...1307....4505....16265.....46773....136935.....481479
.0..162..1079...941...4491...20842....89121....286746...1022779....4520360
.0..421..4064..3316..17828..104969...532511...1932168...7608792...40495097
.0.1103.15183.12016..80293..623549..4281120..17200486..81226394..547173278
.0.2890.55012.34060.304958.3195095.26823700.120221024.683140749.5901256655
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) +2*a(n-3) -a(n-4)
k=3: [order 16]
k=4: [order 72] for n>73
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 16] for n>18
n=4: [order 68] for n>69
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..1..1..1. .0..0..1..1. .0..1..0..1. .0..1..1..0
..1..0..1..0. .1..0..0..0. .0..0..1..1. .1..0..1..0. .0..0..0..0
..0..1..0..1. .1..1..1..1. .0..1..0..1. .0..1..0..1. .0..1..1..0
..1..0..1..0. .0..1..1..1. .0..1..1..0. .1..0..1..0. .0..0..0..0
..1..1..1..1. .1..0..0..0. .1..0..0..1. .0..0..0..0. .0..1..1..0
CROSSREFS
Column 2 is A185828.
Column 4 is A302274.
Row 1 is A000045(n-1).
Row 2 is A302279.
Row 3 is A302280.
Sequence in context: A085550 A223139 A302278 * A302528 A303410 A126671
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 12 2018
STATUS
approved