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 1-3 of 3 results.

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

Crossrefs

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

Crossrefs

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

Crossrefs

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 1-3 of 3 results.