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A262917
T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row divisible by 3 and each column divisible by 7, read as a binary number with top and left being the most significant bits.
11
1, 1, 2, 1, 3, 3, 1, 6, 5, 5, 1, 11, 15, 9, 10, 1, 22, 33, 53, 27, 19, 1, 43, 99, 137, 318, 61, 37, 1, 86, 261, 853, 1411, 1207, 145, 74, 1, 171, 783, 2953, 18190, 7417, 5797, 435, 147, 1, 342, 2241, 17333, 121507, 152587, 51769, 34782, 1253, 293, 1, 683, 6723, 71721
OFFSET
1,3
COMMENTS
Table starts
...1....1.......1........1...........1...........1............1...........1
...2....3.......6.......11..........22..........43...........86.........171
...3....5......15.......33..........99.........261..........783........2241
...5....9......53......137.........853........2953........17333.......71721
..10...27.....318.....1411.......18190......121507......1444558....12031011
..19...61....1207.....7417......152587.....1550557.....30497815...420921961
..37..145....5797....51769.....2045269....33948145...1282949605.32134185721
..74..435...34782...529931....42299374..1361585275.102437680622
.147.1253..189135..4701201...727767387.42115306149
.293.3593.1089701.44632313.13958567845
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4)
k=2: [order 15]
k=3: [order 15]
Empirical for row n:
n=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
n=3: a(n) = 3*a(n-1) +3*a(n-2) -9*a(n-3)
n=4: [order 8]
n=5: [order 10]
n=6: [order 65]
EXAMPLE
Some solutions for n=4 k=4
..0..0..1..1..0....0..1..1..1..1....1..0..0..1..0....0..0..0..0..0
..1..1..0..0..0....0..1..1..0..0....1..1..0..0..0....0..0..0..0..0
..1..1..1..1..0....0..1..1..1..1....1..1..0..1..1....0..0..1..1..0
..1..1..0..0..0....0..0..0..0..0....0..1..0..0..1....0..0..1..1..0
..0..0..1..1..0....0..0..0..1..1....0..0..0..1..1....0..0..1..1..0
CROSSREFS
Column 1 is A046630(n-1).
Column 2 is A262314(n-1).
Row 2 is A005578(n+1).
Row 3 is A262326.
Sequence in context: A127119 A322265 A066704 * A165007 A284979 A127123
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Oct 04 2015
STATUS
approved