|
| |
|
|
A232316
|
|
T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero
|
|
14
|
|
|
|
2, 5, 5, 16, 24, 13, 52, 139, 115, 34, 169, 853, 1202, 551, 89, 549, 5241, 14042, 10409, 2640, 233, 1784, 32089, 164014, 231454, 90157, 12649, 610, 5797, 196698, 1905436, 5142441, 3815483, 780922, 60605, 1597, 18837, 1205422, 22161823, 113293694
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Table starts
.....2.......5.........16............52..............169.................549
.....5......24........139...........853.............5241...............32089
....13.....115.......1202.........14042...........164014.............1905436
....34.....551......10409........231454..........5142441...........113293694
....89....2640......90157.......3815483........161243887..........6736602042
...233...12649.....780922......62897985.......5055954492........400571676322
...610...60605....6764246....1036869496.....158534446141......23818815015639
..1597..290376...58591124...17092731689....4971005036586....1416315842358249
..4181.1391275..507509767..281772661177..155870804492221...84217060496525106
.10946.6665999.4395993154.4645005493684.4887484036570530.5007720081104988709
|
|
|
LINKS
|
R. H. Hardin, Table of n, a(n) for n = 1..390
|
|
|
FORMULA
|
Empirical for column k:
k=1: a(n) = 3*a(n-1) -a(n-2)
k=2: a(n) = 5*a(n-1) -a(n-2)
k=3: a(n) = 10*a(n-1) -11*a(n-2) -5*a(n-3) -a(n-4)
k=4: a(n) = 19*a(n-1) -44*a(n-2) +43*a(n-3) -19*a(n-4) +4*a(n-5) -2*a(n-6) for n>7
k=5: [order 12] for n>13
k=6: [order 18] for n>20
k=7: [order 37] for n>40
Empirical for row n:
n=1: a(n) = 3*a(n-1) +a(n-2) -2*a(n-4) for n>5
n=2: [order 12] for n>14
n=3: [order 32] for n>34
n=4: [order 78] for n>82
|
|
|
EXAMPLE
|
Some.solutions.for.n=3.k=4
..0..0..0..1..1....0..0..1..1..0....0..0..0..1..1....0..0..1..1..0
..0..0..1..1..1....0..1..1..0..0....0..0..0..1..1....0..1..1..0..1
..1..1..0..0..0....1..0..0..1..1....0..0..1..1..1....0..0..0..1..0
..1..1..1..1..1....1..1..1..0..0....0..0..0..0..0....1..1..1..0..0
|
|
|
CROSSREFS
|
Column 1 is A001519(n+1)
Column 2 is A004254(n+1)
Sequence in context: A063786 A121304 A002106 * A184604 A064630 A089793
Adjacent sequences: A232313 A232314 A232315 * A232317 A232318 A232319
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
R. H. Hardin, Nov 22 2013
|
|
|
STATUS
|
approved
|
| |
|
|
