A271209 -id:A271209 - cp's OEIS frontend

A131471 a(n) = n^5+n.

0, 2, 34, 246, 1028, 3130, 7782, 16814, 32776, 59058, 100010, 161062, 248844, 371306, 537838, 759390, 1048592, 1419874, 1889586, 2476118, 3200020, 4084122, 5153654, 6436366, 7962648, 9765650, 11881402, 14348934, 17210396, 20511178, 24300030, 28629182, 33554464

Offset: 0

Mohammad K. Azarian, Jul 27 2007

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A002378, A007531, A034262, A091940, A058895, A059826.

Cf. A271208, A271209.

[n^5+n: n in [0..30]]; // Vincenzo Librandi, Oct 01 2011

Table[n^5 + n, {n, 0, 50}] (* Paolo Xausa, Nov 03 2024 *)

a(n) = n^5+n; \\ Michel Marcus, Apr 02 2016

G.f.: 2*x*(1+11*x+36*x^2+11*x^3+x^4)/(-1+x)^6. - R. J. Mathar, Nov 14 2007

a(n) = A271208(n) + 1 = A271209(n) - 1. - Paolo Xausa, Nov 03 2024

A271208 a(n) = n^5 + n - 1.

Original entry on oeis.org

-1, 1, 33, 245, 1027, 3129, 7781, 16813, 32775, 59057, 100009, 161061, 248843, 371305, 537837, 759389, 1048591, 1419873, 1889585, 2476117, 3200019, 4084121, 5153653, 6436365, 7962647, 9765649, 11881401, 14348933, 17210395, 20511177, 24300029, 28629181, 33554463

Offset: 0

Jaroslav Krizek, Apr 02 2016

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A003627, A016789, A131471, A161945, A271209.

Magma
```
[n^5+n-1: n in [0..100]];
```

A271208:=n->n^5 + n - 1: seq(A271208(n), n=0..40); # Wesley Ivan Hurt, Apr 02 2016

Table[n^5+n-1, {n, 0, 100}] (* Waldemar Puszkarz, Apr 02 2016 *)
LinearRecurrence[{6,-15,20,-15,6,-1},{-1,1,33,245,1027,3129},40] (* Harvey P. Dale, Sep 02 2020 *)

for(n=0, 100, print1(n^5+n-1, ", ")) \\ Waldemar Puszkarz, Apr 02 2016

a(n) = A271209(n) - 2.
From Wesley Ivan Hurt, Apr 02 2016: (Start)
G.f.: (-1 + 7*x + 12*x^2 + 82*x^3 + 17*x^4 + 3*x^5) / (x-1)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5)- a (n-6), n > 5. (End)
a(n) = A131471(n) - 1. - Omar E. Pol, Apr 05 2016

A272162 a(n) = n^5-n+1.

Original entry on oeis.org

1, 1, 31, 241, 1021, 3121, 7771, 16801, 32761, 59041, 99991, 161041, 248821, 371281, 537811, 759361, 1048561, 1419841, 1889551, 2476081, 3199981, 4084081, 5153611, 6436321, 7962601, 9765601, 11881351, 14348881, 17210341, 20511121, 24299971, 28629121, 33554401, 39135361, 45435391

Offset: 0

Benjamin Przybocki, Apr 23 2016

This is the simplest polynomial whose roots cannot be expressed in terms of radicals.

Wikipedia, Finding roots of a quintic equation
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Cf. A271209

Table[n^5 - n + 1, {n, 0, 34}] (* Michael De Vlieger, Apr 26 2016 *)

G.f.: ( 1-5*x+40*x^2+50*x^3+35*x^4-x^5 ) / (x-1)^6. - R. J. Mathar, Apr 26 2016

cp's OEIS Frontend

A131471 a(n) = n^5+n.

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A271208 a(n) = n^5 + n - 1.

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A272162 a(n) = n^5-n+1.

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