cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A180356 a(n) = n^6 + 6n.

Original entry on oeis.org

0, 7, 76, 747, 4120, 15655, 46692, 117691, 262192, 531495, 1000060, 1771627, 2986056, 4826887, 7529620, 11390715, 16777312, 24137671, 34012332, 47045995, 64000120, 85766247, 113380036, 148036027, 191103120, 244140775, 308915932
Offset: 0

Views

Author

Odimar Fabeny, Aug 30 2010

Keywords

Links

Crossrefs

Cf. A079908, A132411, A180354, A180355.

Programs

  • Magma
    [n^6+6*n : n in [0..50]]; // Wesley Ivan Hurt, Jul 07 2025
  • Mathematica
    Table[n^6+6n,{n,0,30}] (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,7,76,747,4120,15655,46692},30] (* Harvey P. Dale, Feb 14 2023 *)

Formula

a(n) = +7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) +a(n-7). G.f.: x*(-7-27*x-362*x^2-242*x^3-87*x^4+5*x^5)/(x-1)^7. - R. J. Mathar, Sep 24 2010

Extensions

First term corrected by Odimar Fabeny, Sep 23 2010
a(0) corrected by R. J. Mathar, Sep 24 2010

A180357 a(n) = n^7 + 7*n.

Original entry on oeis.org

0, 8, 142, 2208, 16412, 78160, 279978, 823592, 2097208, 4783032, 10000070, 19487248, 35831892, 62748608, 105413602, 170859480, 268435568, 410338792, 612220158, 893871872, 1280000140, 1801088688, 2494358042
Offset: 0

Views

Author

Odimar Fabeny, Aug 30 2010

Keywords

Links

Crossrefs

Cf. A132411, A079908, A180354, A180355, A180356.

Programs

  • Mathematica
    Table[n^7+7n,{n,0,30}] (* Harvey P. Dale, Sep 10 2010 *)

Formula

From Chai Wah Wu, Oct 15 2016: (Start)
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) for n > 7.
G.f.: 2*x*(4*x^6 + 39*x^5 + 648*x^4 + 1138*x^3 + 648*x^2 + 39*x + 4)/(x - 1)^8. (End)

Extensions

First term corrected and additional terms from Harvey P. Dale, Sep 10 2010

A180358 n^8+8n.

Original entry on oeis.org

0, 9, 272, 6585, 65568, 390665, 1679664, 5764857, 16777280, 43046793, 100000080, 214358969, 429981792, 815730825, 1475789168, 2562890745, 4294967424, 6975757577, 11019960720, 16983563193, 25600000160, 37822859529, 54875873712
Offset: 0

Views

Author

Odimar Fabeny, Aug 30 2010

Keywords

Links

Crossrefs

Cf.: A132411, A079908, A180354, A180355, A180356, A180357.

Programs

  • Mathematica
    Table[n^8+8n,{n,0,30}] (* or *) LinearRecurrence[ {9,-36,84,-126,126,-84,36,-9,1},{0,9,272,6585,65568,390665,1679664,5764857,16777280},30] (* Harvey P. Dale, Jan 03 2012 *)

Formula

a(n)= +9*a(n-1) -36*a(n-2) +84*a(n-3) -126*a(n-4) +126*a(n-5) -84*a(n-6) +36*a(n-7) -9*a(n-8) +a(n-9). G.f.: x*(-9-191*x-4461*x^2-15339*x^3-15899*x^4-4125*x^5-303*x^6+7*x^7) / (x-1)^9 . [From R. J. Mathar, Sep 19 2010]

Extensions

a(0) corrected by R. J. Mathar, Sep 19 2010

A180359 n^9+9n.

Original entry on oeis.org

0, 10, 530, 19710, 262180, 1953170, 10077750, 40353670, 134217800, 387420570, 1000000090, 2357947790, 5159780460, 10604499490, 20661046910, 38443359510, 68719476880, 118587876650, 198359290530, 322687697950, 512000000180
Offset: 0

Views

Author

Odimar Fabeny, Aug 30 2010

Keywords

Links

Crossrefs

Cf. A132411, A079908, A180354, A180355, A180356, A180357, A180358.

Formula

a(n)= +10*a(n-1) -45*a(n-2) +120*a(n-3) -210*a(n-4) +252*a(n-5) -210*a(n-6) +120*a(n-7) -45*a(n-8) +10*a(n-9) -a(n-10). G.f.: 10*x*(1+43*x+1486*x^2+8773*x^3+15682*x^4+8773*x^5+1486*x^6+43*x^7+x^8)/(x -1)^10. [From R. J. Mathar, Sep 19 2010]

Extensions

a(0) corrected by R. J. Mathar, Sep 19 2010
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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