A024075 -id:A024075 - cp's OEIS frontend

A208704 Number of nX3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

4, 28, 196, 1372, 9604, 67228, 470596, 3294172, 23059204, 161414428, 1129900996, 7909306972, 55365148804, 387556041628, 2712892291396, 18990246039772, 132931722278404, 930522055948828, 6513654391641796, 45595580741492572

Offset: 1

R. H. Hardin, Mar 01 2012

nonn

Column 3 of A208709.

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

R. H. Hardin, Table of n, a(n) for n = 1..210

Cf. A270471.

Empirical: a(n) = 7*a(n-1).

Empirical: a(n) = (A198480(n)+1)*2 = (A024075(n)+1)*4. [Martin Ettl, Nov 09 2012; revised Nov 13 2012]

A198689 8*7^n-1.

Original entry on oeis.org

7, 55, 391, 2743, 19207, 134455, 941191, 6588343, 46118407, 322828855, 2259801991, 15818613943, 110730297607, 775112083255, 5425784582791, 37980492079543, 265863444556807, 1861044111897655, 13027308783283591, 91191161482985143

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-7).

Cf. A024075, A048473, A081655, A198480, A198647.

Magma
```
[8*7^n-1: n in [0..30]]
```

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.

G.f. ( 7-x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198690 9*7^n-1.

Original entry on oeis.org

8, 62, 440, 3086, 21608, 151262, 1058840, 7411886, 51883208, 363182462, 2542277240, 17795940686, 124571584808, 872001093662, 6104007655640, 42728053589486, 299096375126408, 2093674625884862, 14655722381194040, 102590056668358286

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-7).

Cf. A024075, A048473, A081655, A198480, A198647.

Magma
```
[9*7^n-1: n in [0..30]]
```

9*7^Range[0,30]-1 (* or *) LinearRecurrence[{8,-7},{8,62},30] (* Harvey P. Dale, Apr 22 2019 *)

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.

G.f. ( 8-2*x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198691 10*7^n-1.

Original entry on oeis.org

9, 69, 489, 3429, 24009, 168069, 1176489, 8235429, 57648009, 403536069, 2824752489, 19773267429, 138412872009, 968890104069, 6782230728489, 47475615099429, 332329305696009, 2326305139872069, 16284135979104489, 113988951853731429

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-7).

Cf. A024075, A048473, A081655, A198480, A198647.

Magma
```
[10*7^n-1: n in [0..30]]
```

10*7^Range[0,20]-1 (* or *) LinearRecurrence[{8,-7},{9,69},20] (* Harvey P. Dale, Mar 30 2016 *)

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.

G.f. ( 9-3*x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198692 a(n) = 11*7^n-1.

Original entry on oeis.org

10, 76, 538, 3772, 26410, 184876, 1294138, 9058972, 63412810, 443889676, 3107227738, 21750594172, 152254159210, 1065779114476, 7460453801338, 52223176609372, 365562236265610, 2558935653859276, 17912549577014938

Offset: 0

Vincenzo Librandi, Oct 29 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (8,-7).

Cf. A024075, A048473, A081655, A198480, A198647.

Magma
```
[11*7^n-1: n in [0..30]]
```

11 (7^Range[0, 30]) - 1 (* Wesley Ivan Hurt, Jan 21 2017 *)

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.

G.f.: ( 10-4*x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

cp's OEIS Frontend

A208704 Number of nX3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

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A198689 8*7^n-1.

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A198690 9*7^n-1.

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A198691 10*7^n-1.

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A198692 a(n) = 11*7^n-1.

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