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.

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

R. H. Hardin, Table of n, a(n) for n = 1..112

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

Adjacent sequences: A262914 A262915 A262916 * A262918 A262919 A262920

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 04 2015

Status

approved