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.

A240931 a(n) = n^8 - n^7.

Original entry on oeis.org

0, 0, 128, 4374, 49152, 312500, 1399680, 4941258, 14680064, 38263752, 90000000, 194871710, 394149888, 752982204, 1370375552, 2392031250, 4026531840, 6565418768, 10407740544, 16089691302, 24320000000, 36021770820, 52381515648, 74906159834, 105488842752, 146484375000
Offset: 0

Views

Author

Martin Renner, Aug 03 2014

Keywords

Comments

For n>1 number of 8-digit positive integers in base n.

Links

Crossrefs

Cf. A001015, A001016.
Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240932, A240933.

Programs

  • Magma
    [n^8-n^7 : n in [0..30]]; // Wesley Ivan Hurt, Aug 09 2014
  • Maple
    A240931:=n->n^8-n^7: seq(A240931(n), n=0..30); # Wesley Ivan Hurt, Aug 09 2014
  • Mathematica
    Table[n^8 - n^7, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 09 2014 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{0,0,128,4374,49152,312500,1399680,4941258,14680064},30] (* Harvey P. Dale, Apr 29 2016 *)
  • PARI
    vector(100, n, (n-1)^8 - (n-1)^7) \\ Derek Orr, Aug 03 2014
  • PARI
    concat([0,0], Vec(-2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9 + O(x^100))) \\ Colin Barker, Aug 08 2014

Formula

a(n) = n^7*(n-1) = n^8 - n^7.
a(n) = A001016(n) - A001015(n).
G.f.: -2*x^2*(x^6+183*x^5+2682*x^4+8422*x^3+7197*x^2+1611*x+64) / (x-1)^9. - Colin Barker, Aug 08 2014
Sum_{n>=2} 1/a(n) = 7 - Sum_{k=2..7} zeta(k). - Amiram Eldar, Jul 05 2020

A240932 a(n) = n^9 - n^8.

Original entry on oeis.org

0, 0, 256, 13122, 196608, 1562500, 8398080, 34588806, 117440512, 344373768, 900000000, 2143588810, 4729798656, 9788768652, 19185257728, 35880468750, 64424509440, 111612119056, 187339329792, 305704134738, 486400000000, 756457187220, 1152393344256, 1722841676182
Offset: 0

Views

Author

Martin Renner, Aug 03 2014

Keywords

Comments

For n>1 number of 9-digit positive integers in base n.

Links

Crossrefs

Cf. A001016, A001017.
Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240931, A240933.

Programs

Formula

a(n) = n^8*(n-1) = n^9 - n^8.
a(n) = A001017(n) - A001016(n).
G.f.: 2*x^2*(x^7+374*x^6+9327*x^5+49780*x^4+78095*x^3+38454*x^2+5281*x+128) / (x-1)^10. - Colin Barker, Aug 08 2014
Sum_{n>=2} 1/a(n) = 8 - Sum_{k=2..8} zeta(k). - Amiram Eldar, Jul 05 2020

A240933 a(n) = n^10 - n^9.

Original entry on oeis.org

0, 0, 512, 39366, 786432, 7812500, 50388480, 242121642, 939524096, 3099363912, 9000000000, 23579476910, 56757583872, 127253992476, 268593608192, 538207031250, 1030792151040, 1897406023952, 3372107936256, 5808378560022, 9728000000000, 15885600931620, 25352653573632
Offset: 0

Views

Author

Martin Renner, Aug 03 2014

Keywords

Comments

For n>1 number of 10-digit positive integers in base n.

Links

Crossrefs

Cf. A001017, A008454.
Cf. A002378, A045991, A085537, A085538, A085539, A240930, A240931, A240932.

Programs

  • Magma
    [n^10-n^9 : n in [0..30]]; // Wesley Ivan Hurt, Aug 03 2014
  • Maple
    A240933:=n->n^10-n^9: seq(A240933(n), n=0..30); # Wesley Ivan Hurt, Aug 03 2014
  • Mathematica
    Table[n^10 - n^9, {n, 0, 30}] (* Wesley Ivan Hurt, Aug 03 2014 *)
CoefficientList[Series[2 (256*x^2 + 16867*x^3 + 190783*x^4 + 621199*x^5 + 689155*x^6 + 264409*x^7 + 30973*x^8 + 757*x^9 + x^10)/(1 - x)^11, {x, 0, 30}], x] (* Wesley Ivan Hurt, Aug 03 2014 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,0,512,39366,786432,7812500,50388480,242121642,939524096,3099363912,9000000000},40] (* Harvey P. Dale, Oct 19 2022 *)
  • PARI
    vector(100, n, (n-1)^10 - (n-1)^9) \\ Derek Orr, Aug 03 2014

Formula

a(n) = n^9*(n-1) = n^10 - n^9.
a(n) = A008454(n) - A001017(n). - Michel Marcus, Aug 03 2014
G.f.: 2*(256*x^2 + 16867*x^3 + 190783*x^4 + 621199*x^5 + 689155*x^6 + 264409*x^7 + 30973*x^8 + 757*x^9 + x^10)/(1 - x)^11. - Wesley Ivan Hurt, Aug 03 2014
Recurrence: a(n) = 11*a(n-1)-55*a(n-2)+165*a(n-3)-330*a(n-4)+462*a(n-5)-462*a(n-6)+330*a(n-7)-165*a(n-8)+55*a(n-9)-11*a(n-10)+a(n-11). - Wesley Ivan Hurt, Aug 03 2014
Sum_{n>=2} 1/a(n) = 9 - Sum_{k=2..9} zeta(k). - Amiram Eldar, Jul 05 2020
Showing 1-3 of 3 results.

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