A014052 -id:A014052 - cp's OEIS frontend

A197598 Floor((9n+1/n)^n).

10, 342, 20421, 1726760, 188665362, 25257633873, 4001931082417, 732295911309956, 151957855559538858, 35257207352182955134, 9044237131202445725077, 2541585712463861383036826, 776473970630759909605090447, 256232041409079180707274204957

Offset: 1

Vincenzo Librandi, Oct 17 2011

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

Cf. A014052.

Magma
```
[Floor((9*n+1/n)^n): n in [1..20]]
```

Table[Floor[(9n+1/n)^n],{n,20}] (* Harvey P. Dale, Nov 07 2019 *)

a(n)=floor((9*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

A197599 Floor((10n+1/n)^n).

Original entry on oeis.org

11, 420, 27910, 2624602, 318800200, 47439020041, 8353801755006, 1698808167100875, 391746480089540115, 101004512021025221012, 28791615763253886202480, 8990685731188213404550238, 3052132045866636492112058599, 1119164206256115117485135326641, 440822282742124422495281791483358

Offset: 1

Vincenzo Librandi, Oct 17 2011

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

Cf. A014052.

Magma
```
[Floor((10*n+1/n)^n): n in [1..20]];
```

a(n)=floor((10*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

A197600 Floor((11n+1/n)^n).

Original entry on oeis.org

12, 506, 37037, 3834008, 512501792, 83914215402, 16258109291002, 3637416562713075, 922786228220640101, 261741863272493596614, 82078032321730681299097, 28195269239973685901676782, 10529425953839699619063326835, 4247266693140960691762845677068

Offset: 1

Vincenzo Librandi, Oct 17 2011

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

Cf. A014052.

Magma
```
[Floor((11*n+1/n)^n): n in [1..20]]
```

Table[Floor[(11*n + 1/n)^n], {n, 40}] (* T. D. Noe, Dec 27 2011 *)

a(n)=floor((11*n+1/n)^n) \\ Charles R Greathouse IV, Dec 27 2011

A197605 Floor( ( n + 1/n )^6 ).

Original entry on oeis.org

64, 244, 1371, 5892, 19770, 54992, 132810, 287700, 572042, 1061520, 1861242, 3112580, 5000730, 7762992, 11697770, 17174292, 24643050, 34646960, 47833242, 64966020, 86939642, 114792720, 149722890, 193102292, 246493770, 311667792, 390620090, 485590020

Offset: 1

Vincenzo Librandi, Oct 18 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Cf. A014052, A197602, A197603, A197604.

Magma
```
[Floor((n+1/n)^6): n in [1..40]]
```

Table[Floor[(n + 1/n)^6], {n, 40}] (* T. D. Noe, Dec 27 2011 *)
CoefficientList[Series[(64 - 204 x + 1007 x^2 - 821 x^3 + 1017 x^4 - 455 x^5 + 125 x^6 - 15 x^7 + 3 x^8 - x^9) / (1 - x)^7, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2014 *)

a(n)=if(n>3,n^6+6*n^4+15*n^2+20,[64,244,1371][n]) \\ Charles R Greathouse IV, Dec 27 2011

For n > 3, a(n) = n^6 + 6n^4 + 15n^2 + 20. [Charles R Greathouse IV, Dec 27 2011]

G.f.: x*(64-204*x+1007*x^2-821*x^3+1017*x^4-455*x^5+125*x^6-15*x^7+3*x^8-x^9)/(1-x)^7. - Vincenzo Librandi, Dec 18 2014

A197708 a(n) = floor((n + 1/n)^7).

Original entry on oeis.org

128, 610, 4572, 25045, 102807, 339119, 948645, 2337564, 5211939, 10721353, 20642867, 37610342, 65394162, 109236388, 176246402, 275862066, 420381442, 625570111, 911349137, 1302568701, 1829872465, 2530657691, 3450136161, 4642500937, 6172204001, 8115349815

Offset: 1

Vincenzo Librandi, Oct 18 2011

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Cf. A014052, A197602, A197603, A197604.

Magma
```
[Floor((n+1/n)^7): n in [1..40]];
```

Table[Floor[(n + 1/n)^7], {n, 40}] (* T. D. Noe, Dec 27 2011 *)

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

For n > 35, a(n) = n^7 + 7*n^5 + 21*n^3 + 35*n. - Charles R Greathouse IV, Dec 27 2011

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Wesley Ivan Hurt, Apr 17 2023

A197714 Floor((n+1/4)^n).

Original entry on oeis.org

1, 5, 34, 326, 3988, 59604, 1052848, 21460092, 495764693, 12800845441, 365323615365, 11419131242070, 387977390372849, 14236659589753581, 561109543344974893, 23640346895461300427, 1060265646084471617079, 50434955069054663240727, 2536202597745552881270240

Offset: 1

Vincenzo Librandi, Oct 18 2011

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

Cf. A014052.

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

Table[Floor[(n + 1/4)^n], {n, 20}] (* T. D. Noe, Dec 27 2011 *)

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

A197322 a(n) = floor((2*n+1/n)^n).

Original entry on oeis.org

3, 20, 254, 4632, 110408, 3243617, 113177496, 4570858599, 209655304352, 10763674952097, 611433842280387, 38071427445729200, 2578294348444597266, 188670154792420320214, 14834716200104606205407, 1247263229999781126495327, 111661618863544248806155259

Offset: 1

Vincenzo Librandi, Oct 17 2011

nonn

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

Cf. A014052.

Magma
```
[Floor((2*n+1/n)^n): n in [1..20]];
```

Table[Floor[(2n+1/n)^n],{n,20}] (* Harvey P. Dale, Mar 25 2018 *)

A197323 Floor((3*n+1/n)^n).

Original entry on oeis.org

4, 42, 813, 22518, 811368, 35946075, 1888624971, 114746269757, 7912720985079, 610470884770406, 52094956940751710, 4871691779130290166, 495409898474358881326, 54427906182810588386673, 6424384909407981686846705, 810777549111969648699638306, 108944087230453697240059783283

Offset: 1

Vincenzo Librandi, Oct 17 2011

nonn

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

Cf. A014052

Magma
```
[Floor((3*n+1/n)^n): n in [1..20]];
```

Table[Floor[(3n+1/n)^n],{n,20}] (* Harvey P. Dale, Dec 16 2012 *)

A197709 Floor((n+1/n)^8).

Original entry on oeis.org

256, 1525, 15241, 106441, 534597, 2091239, 6776036, 18992710, 47486563, 108285670, 228948163, 454458310, 855154435, 1537112038, 2655445795, 4431034438, 7171212835, 11295015910, 17363599363, 26116502470, 38514458563, 55789499110, 79503137635, 111613460038, 154551988195, 211311224038

Offset: 1

Vincenzo Librandi, Oct 18 2011

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A014052, A197602, A197603, A197604

Magma
```
[Floor((n+1/n)^8): n in [1..40]]
```

A197710 Floor((n+1/n)^9).

Original entry on oeis.org

512, 3814, 50805, 452376, 2779905, 12895977, 48400258, 154315775, 432655358, 1093685272, 2539243267, 5491371250, 11182788769, 21629362253, 40008716648, 71173490663, 122332454247, 203937787267, 330822261550, 523635874526, 810637651662, 1229904866745, 1832028823765, 2683373601749

Offset: 1

Vincenzo Librandi, Oct 18 2011

nonn

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Cf. A014052, A197602, A197603, A197604

Magma
```
[Floor((n+1/n)^9): n in [1..40]]
```

Table[Floor[(n+1/n)^9],{n,30}] (* Harvey P. Dale, Aug 26 2022 *)

cp's OEIS Frontend

A197598 Floor((9n+1/n)^n).

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A197599 Floor((10n+1/n)^n).

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Magma

PARI

A197600 Floor((11n+1/n)^n).

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Magma

Mathematica

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A197605 Floor( ( n + 1/n )^6 ).

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Magma

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PARI

Formula

A197708 a(n) = floor((n + 1/n)^7).

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Magma

Mathematica

PARI

Formula

A197714 Floor((n+1/4)^n).

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Magma

Mathematica

PARI

A197322 a(n) = floor((2*n+1/n)^n).

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Keywords

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Programs

Magma

Mathematica

A197323 Floor((3*n+1/n)^n).

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Author

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Programs

Magma

Mathematica