A198647 -id:A198647 - cp's OEIS frontend

A198688 6*7^n-1.

5, 41, 293, 2057, 14405, 100841, 705893, 4941257, 34588805, 242121641, 1694851493, 11863960457, 83047723205, 581334062441, 4069338437093, 28485369059657, 199397583417605, 1395783083923241, 9770481587462693, 68393371112238857

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. A048473, A081655, A198480, A198647.

Magma
```
[6*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. ( 5+x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198686 4*7^n-1.

Original entry on oeis.org

3, 27, 195, 1371, 9603, 67227, 470595, 3294171, 23059203, 161414427, 1129900995, 7909306971, 55365148803, 387556041627, 2712892291395, 18990246039771, 132931722278403, 930522055948827, 6513654391641795, 45595580741492571

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. A048473, A081655, A198480, A198647.

Magma
```
[4*7^n-1: n in [0..30]]
```

4*7^Range[0,20]-1 (* or *) LinearRecurrence[{8,-7},{3,27},20] (* Harvey P. Dale, Dec 27 2011 *)

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

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

A198687 5*7^n-1.

Original entry on oeis.org

4, 34, 244, 1714, 12004, 84034, 588244, 4117714, 28824004, 201768034, 1412376244, 9886633714, 69206436004, 484445052034, 3391115364244, 23737807549714, 166164652848004, 1163152569936034, 8142067989552244, 56994475926865714

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. A048473, A081655, A198480, A198647.

Magma
```
[5*7^n-1: n in [0..30]]
```

CoefficientList[Series[(4+2*x)/((1-x)*(1-7*x)),{x,0,40}],x] (* Vincenzo Librandi, Jul 06 2012 *)
LinearRecurrence[{8,-7},{4,34},20] (* Harvey P. Dale, Jul 23 2024 *)

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

G.f.:(4+2*x)/((1-x)*(1-7*x)). - Vincenzo Librandi, Jul 06 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

A198688 6*7^n-1.

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A198686 4*7^n-1.

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A198687 5*7^n-1.

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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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Magma

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

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Magma

Mathematica

Formula