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

1,3

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A262267(n-1).

Row 2 is A005578(n+1).

Sequence in context: A306186 A154929 A249042 * A049400 A283524 A106382

Adjacent sequences: A262469 A262470 A262471 * A262473 A262474 A262475

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 23 2015

Status

approved