login
A303410
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5 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, 28, 23, 0, 5, 27, 42, 119, 61, 0, 8, 45, 100, 168, 541, 162, 0, 13, 98, 290, 547, 902, 2327, 421, 0, 21, 193, 730, 2079, 4013, 3256, 10384, 1103, 0, 34, 379, 1700, 6322, 29411, 21361, 15852, 47491, 2890, 0, 55, 778, 4246, 17903
OFFSET
1,5
COMMENTS
Table starts
.0....1......1......2.......3.........5..........8..........13............21
.0....3......7.....10......27........45.........98.........193...........379
.0...10.....28.....42.....100.......290........730........1700..........4246
.0...23....119....168.....547......2079.......6322.......17903.........53665
.0...61....541....902....4013.....29411.....160247......660748.......3071197
.0..162...2327...3256...21361....236326....1716995.....8688851......56229035
.0..421..10384..15852..115770...2158662...24386918...158640643....1293822589
.0.1103..47491..77904..803911..27002794..497878411..4298730424...50946692110
.0.2890.208616.314276.4667376.250400003.6748940959.74532460229.1222253462556
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 18]
k=4: [order 72]
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 15] for n>17
n=4: [order 71] for n>72
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..1..1..0. .0..1..0..1. .0..0..0..0. .0..0..0..0
..1..0..1..1. .1..0..0..1. .1..0..1..0. .1..1..1..1. .1..0..1..0
..0..0..0..0. .1..1..1..1. .0..1..0..1. .1..0..1..0. .0..1..0..1
..0..1..0..0. .0..1..1..0. .0..0..0..0. .1..1..0..1. .1..1..1..1
..1..0..1..1. .1..0..0..1. .1..1..1..1. .1..0..1..0. .0..0..0..1
CROSSREFS
Column 2 is A185828.
Column 4 is A302524.
Row 1 is A000045(n-1).
Row 2 is A302279.
Row 3 is A302529.
Sequence in context: A302278 A302728 A302528 * A126671 A209437 A325447
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 23 2018
STATUS
approved