A198480 -id:A198480 - 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

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.

Original entry on oeis.org

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]

A197880 Squarefree part of ((2n-1)!)^(2n-3).

Original entry on oeis.org

1, 6, 30, 35, 70, 77, 3003, 1430, 24310, 230945, 969969, 4056234, 676039, 312018, 1292646, 33393355, 2203961430, 90751353, 3357800061, 1531628098, 156991880045, 5786272150230, 105204948186, 107492012277, 35830670759, 3654728417418, 14900046624858

Offset: 1

Artur Jasinski, Oct 25 2011

nonn

These numbers are quadratic fields of extensions of polynomials of odd degree obtained by taken 2n-1 terms of expansion of e^x in power series at 0. All these polynomials have Galois group S(2n-1) over rationals.

Cf. A007913, A134367, A198481.

A134367 := proc(n)
        (n!)^(n-2) ;
end proc:
A007913 := proc(n)
        a := 1 ;
        for pf in ifactors(n)[2] do
                p := op(1,pf) ;
                e := op(2,pf) ;
                a := a*p^(e mod 2) ;
        end do:
        a ;
end proc:
A198480 := proc(n)
        A007913( A134367(2*n-1)) ;
end proc:
seq(A198480(n),n=1..10) ; # R. J. Mathar, Oct 25 2011

aa = {}; data = Table[kk = Sqrt[(n!)^(n - 2)], {n, 1, 100, 2}]; sp = data /. Sqrt[_] -> 1; sfp = data/sp; sfp^2

a(n) = A007913(A134367(2*n-1)). - R. J. Mathar, Oct 25 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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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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A197880 Squarefree part of ((2n-1)!)^(2n-3).

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Maple

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A198686 4*7^n-1.

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Magma

Mathematica

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A198687 5*7^n-1.

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Magma

Mathematica

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A198689 8*7^n-1.

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Magma

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A198690 9*7^n-1.

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Magma

Mathematica

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A198691 10*7^n-1.

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Magma

Mathematica

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

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