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

Author

R. H. Hardin, Oct 04 2015

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A046630(n-1).

Column 2 is A262314(n-1).

Row 2 is A005578(n+1).

Row 3 is A262326.

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]