A014052 -id:A014052 - cp's OEIS frontend

A014058 a(n) = ceiling((n+1/n)^n).

2, 7, 38, 327, 3803, 54993, 948646, 18992711, 432655359, 11046221255, 312347907387, 9688154906658, 327018557066165, 11932588574197764, 468012768020438831, 19634066192684343923, 877272066059957914874

Offset: 1

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A014052, A014056.

[Ceiling((n+1/n)^n): n in [1..20]]; // Vincenzo Librandi, Oct 18 2011

Table[Ceiling[(n+1/n)^n],{n,20}] (* Harvey P. Dale, Jul 09 2017 *)

a(n)=ceil((n+1/n)^n) \\ Charles R Greathouse IV, Jul 01 2013

[ceil((n+1/n)^n) for n in (1..20)] # G. C. Greubel, Nov 23 2018

A014056 a(n) = round( (n + 1/n)^n ).

Original entry on oeis.org

2, 6, 37, 326, 3802, 54992, 948645, 18992711, 432655358, 11046221254, 312347907386, 9688154906658, 327018557066165, 11932588574197763, 468012768020438830, 19634066192684343923, 877272066059957914874

Offset: 1

N. J. A. Sloane

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A014052, A014058.

[Round((n+1/n)^n): n in [1..20]]; // Vincenzo Librandi, Oct 20 2011

Table[Round[(n+1/n)^n], {n,50}] (* G. C. Greubel, Feb 05 2024 *)

a(n)=round((n+1/n)^n) \\ Charles R Greathouse IV, Jul 01 2013

[round((n+1/n)^n) for n in range(1,51)] # G. C. Greubel, Feb 05 2024

A197602 Floor((n+1/n)^3).

Original entry on oeis.org

8, 15, 37, 76, 140, 234, 364, 536, 756, 1030, 1364, 1764, 2236, 2786, 3420, 4144, 4964, 5886, 6916, 8060, 9324, 10714, 12236, 13896, 15700, 17654, 19764, 22036, 24476, 27090, 29884, 32864, 36036, 39406, 42980, 46764, 50764, 54986, 59436, 64120, 69044, 74214, 79636, 85316, 91260, 97474, 103964, 110736, 117796, 125150

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Cf. A079908, A014052.

Magma
```
[Floor((n+1/n)^3): n in [1..60]]
```

a(n)=n^3+3*n+(3*n^2+1)\n^3 \\ Charles R Greathouse IV, Oct 07 2015

From Bruno Berselli, Oct 17 2011: (Start)
G.f.: x*(8-17*x+25*x^2-14*x^3+6*x^4-3*x^5+x^6)/(1-x)^4.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>7.
a(n) = A079908(n) for n>3. (End)

A197603 a(n) = floor((n+1/n)^4).

Original entry on oeis.org

16, 39, 123, 326, 731, 1446, 2603, 4358, 6891, 10406, 15131, 21318, 29243, 39206, 51531, 66566, 84683, 106278, 131771, 161606, 196251, 236198, 281963, 334086, 393131, 459686, 534363, 617798, 710651, 813606, 927371, 1052678, 1190283, 1340966, 1505531, 1684806, 1879643, 2090918, 2319531, 2566406, 2832491, 3118758

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A010000, A014052.

Magma
```
[Floor((n+1/n)^4): n in [1..60]];
```

Table[Floor[(n+1/n)^4],{n,50}] (* or *) LinearRecurrence[{5,-10,10,-5,1},{16,39,123,326,731,1446,2603},50] (* Harvey P. Dale, Jun 03 2015 *)

a(n)=floor((n+1/n)^4) \\ Charles R Greathouse IV, Oct 07 2015

From Bruno Berselli, Oct 17 2011: (Start)
  G.f.: x*(16-41*x+88*x^2-59*x^3+21*x^4-x^6)/(1-x)^5.
  a(n) = (n^2+2)^2+2 for n>2, a(1)=16, a(2)=39.
  a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5) for n=6 and n>7.
  a(n) = A010000(A010000(n)) for n>2. (End)

A197604 a(n) = floor((n+1/n)^5).

Original entry on oeis.org

32, 97, 411, 1386, 3802, 8917, 18593, 35409, 62785, 105101, 167816, 257592, 382408, 551684, 776400, 1069216, 1444592, 1918908, 2510584, 3240200, 4130616, 5207092, 6497408, 8031984, 9844000, 11969516, 14447592, 17320408, 20633384, 24435300, 28778416, 33718592, 39315408, 45632284, 52736600, 60699816, 69597592, 79509908

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A014052.

Magma
```
[Floor((n+1/n)^5): n in [1..60]]
```

Join[{32,97,411,1386,3802,8917,18593,35409,62785,105101},LinearRecurrence[{6,-15,20,-15,6,-1},{167816,257592,382408,551684,776400,1069216},30]] (* Harvey P. Dale, Jan 16 2015 *)

a(n)=floor((n+1/n)^5) \\ Charles R Greathouse IV, Oct 27 2011

From Bruno Berselli, Oct 27 2011: (Start)
G.f.: x*(32-95*x+309*x^2-265*x^3+191*x^4-62*x^5+16*x^6-13*x^7+11*x^8-5*x^9+5*x^11-10*x^12+10*x^13-5*x^14+x^15)/(1-x)^6.
a(n) = n*(n^4+5*n^2+10) + A033330(n)  for n>1.
a(n) = A197904(n) - 1  for n>1. (End)

A197595 Floor((6n+1/n)^n).

Original entry on oeis.org

7, 156, 6162, 345817, 25120872, 2237952687, 236084694122, 28771727614749, 3977205817386552, 614815375624938276, 105089416995538138497, 19679693805738843682350, 4006775128162674717660621, 881207085092349552894218729, 208190711541113653367733416163

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A014052.

Magma
```
[Floor((6*n+1/n)^n): n in [1..20]];
```

Table[Floor[(6n+1/n)^n],{n,20}] (* Harvey P. Dale, Dec 29 2024 *)

a(n)=floor((6*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

A197324 a(n) = floor((4*n+1/n)^n).

Original entry on oeis.org

5, 72, 1876, 69729, 3363232, 199205126, 13982257728, 1134344816184, 104416147080711, 10750872867074586, 1224163955433850943, 152733676280699540998, 20719969553916698313304, 3036565789908881887393113, 478082645334119488823777214, 80475210949356295594385157620

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A014052.

Magma
```
[Floor((4*n+1/n)^n): n in [1..20]]
```

Table[Floor[(4n+1/n)^n],{n,20}] (* Harvey P. Dale, Mar 23 2012 *)

a(n)=floor((4*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

A197325 Floor((5n+1/n)^n).

Original entry on oeis.org

6, 110, 3605, 168151, 10162550, 753640010, 66200225626, 6719243243859, 773662803646264, 99627047203913814, 14186632841753756405, 2213340465298424454702, 375449162169269152689331, 68797650004483898373052060, 13542753444466024362689788808

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A014052.

Magma
```
[Floor((5*n+1/n)^n): n in [1..20]];
```

Floor[Table[(5n+1/n)^n,{n,20}]] (* Harvey P. Dale, Sep 15 2023 *)

a(n)=floor((5*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

A197596 a(n) = Floor((7n+1/n)^n).

Original entry on oeis.org

8, 210, 9709, 636903, 54039748, 5621026396, 692186010834, 98457959756722, 15883727818630151, 2865366503771469410, 571524481184700575469, 124887520213444076248619, 29669385469799155774434098, 7613687050766411443598268998

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..300

Cf. A014052.

Magma
```
[Floor((7*n+1/n)^n): n in [1..20]];
```

a(n)=floor((7*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

A197597 Floor((8n+1/n)^n).

Original entry on oeis.org

9, 272, 14408, 1081730, 104985728, 12487616538, 1758172862979, 285903205720512, 52725376090628155, 10872393464815690143, 2478802987043990078456, 619122710473385614426209, 168115507427305189329095427, 49309285630177314887251611600

Offset: 1

Vincenzo Librandi, Oct 17 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..250

Cf. A014052.

Magma
```
[Floor((8*n+1/n)^n): n in [1..20]]
```

Table[Floor[(8 n + 1/n)^n], {n, 20}] (* Harvey P. Dale, Dec 25 2017 *)

a(n)=floor((8*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

cp's OEIS Frontend

A014058 a(n) = ceiling((n+1/n)^n).

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A014056 a(n) = round( (n + 1/n)^n ).

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SageMath

A197602 Floor((n+1/n)^3).

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A197603 a(n) = floor((n+1/n)^4).

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A197604 a(n) = floor((n+1/n)^5).

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Magma

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Formula

A197595 Floor((6n+1/n)^n).

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Magma

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A197324 a(n) = floor((4*n+1/n)^n).

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Magma

Mathematica

PARI

A197325 Floor((5n+1/n)^n).

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