login
A232257
T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every element both >= and <= some horizontal or antidiagonal neighbor
16
9, 37, 37, 215, 421, 163, 1287, 6189, 4711, 723, 7673, 96999, 175431, 52779, 3209, 45709, 1532151, 7258599, 4987471, 591181, 14245, 272417, 24091773, 304291873, 544777651, 141815403, 6622029, 63235, 1623601, 379188715, 12652519297
OFFSET
1,1
COMMENTS
Table starts
.....9......37........215..........1287.............7673...............45709
....37.....421.......6189.........96999..........1532151............24091773
...163....4711.....175431.......7258599........304291873.........12652519297
...723...52779....4987471.....544777651......60698037193.......6678855359891
..3209..591181..141815403...40896843985...12109668893083....3525883938158361
.14245.6622029.4032714105.3070212041183.2416017612073105.1861384207351560027
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 4*a(n-1) +2*a(n-2) -a(n-4)
k=2: a(n) = 10*a(n-1) +14*a(n-2) -6*a(n-3) -a(n-4)
k=3: [order 9] for n>10
k=4: [order 21]
k=5: [order 51] for n>54
Empirical for row n:
n=1: [linear recurrence of order 12] for n>13
n=2: [order 56] for n>58
EXAMPLE
Some solutions for n=3 k=4
..0..0..0..0..1....0..0..0..0..2....0..0..0..0..0....0..0..0..1..1
..0..0..0..1..0....0..0..0..2..1....0..0..0..2..2....0..0..1..1..1
..1..2..2..0..2....1..1..1..1..1....1..2..2..2..2....0..1..0..2..1
..1..1..1..2..2....2..2..2..1..1....2..2..1..1..1....1..0..2..1..1
CROSSREFS
Cf. A232258 (row 1), A232259 (row 2), A232260 (row 3), A232261 (row 4), A232262 (row 5), A232263 (row 6), A232250 (column 1), A232251 (column 2).
Sequence in context: A053949 A071134 A116108 * A091961 A103758 A274769
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 21 2013
STATUS
approved