A262472 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with each row divisible by 3 and each column divisible by 5, read as a binary number with top and left being the most significant bits.

1, 1, 2, 1, 3, 4, 1, 6, 9, 7, 1, 11, 36, 17, 13, 1, 22, 121, 115, 37, 26, 1, 43, 484, 457, 469, 107, 52, 1, 86, 1849, 3055, 2413, 2622, 321, 103, 1, 171, 7396, 16081, 30229, 22907, 15732, 865, 205, 1, 342, 29241, 107731, 234421, 552430, 239281, 85723, 2449, 410, 1

Offset: 1

Author

R. H. Hardin, Sep 23 2015

Keywords

• nonn
• tabl

Comments

Table starts

...1....1.......1.........1...........1............1............1............1

...2....3.......6........11..........22...........43...........86..........171

...4....9......36.......121.........484.........1849.........7396........29241

...7...17.....115.......457........3055........16081.......107731.......655001

..13...37.....469......2413.......30229.......234421......2924245.....29005981

..26..107....2622.....22907......552430......8080915....194647694...3858564731

..52..321...15732....239281....11489332....326748241..15659602612.630055962801

.103..865...85723...2028469...198237391..10190636521.997197229531

.205.2449..494605..19072681..3805146805.367750753321

.410.7299.2942190.195594107.77803476910

Examples

			Some solutions for n=4 k=4
..0..0..0..0..0....0..0..0..0..0....0..1..1..0..0....0..1..0..0..1
..0..1..0..0..1....0..1..1..0..0....0..1..0..0..1....0..0..0..1..1
..0..0..0..0..0....0..1..0..0..1....0..1..1..1..1....0..1..0..0..1
..0..1..0..0..1....0..1..1..0..0....0..1..0..0..1....0..0..0..1..1
..0..0..0..0..0....0..1..0..0..1....0..0..0..1..1....0..0..0..0..0
		

Links

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

Crossrefs

Column 1 is A262267(n-1).

Row 2 is A005578(n+1).

Formula

Empirical for column k:

k=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)

k=2: [order 8]

k=3: [order 15]

k=4: [order 73]

Empirical for row n:

n=1: a(n) = a(n-1)

n=2: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)

n=3: a(n) = 4*a(n-1) +5*a(n-2) -20*a(n-3) -4*a(n-4) +16*a(n-5)

n=4: [order 13]

n=5: [order 33]

n=6: [order 67]