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 1-6 of 6 results.

A024077 a(n) = 7^n - n^2.

Original entry on oeis.org

1, 6, 45, 334, 2385, 16782, 117613, 823494, 5764737, 40353526, 282475149, 1977326622, 13841287057, 96889010238, 678223072653, 4747561509718, 33232930569345, 232630513986918, 1628413597910125, 11398895185372782
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. similar sequences listed in A024025.

Programs

  • Magma
    [7^n-n^2: n in [0..25]]; // Vincenzo Librandi, Jul 03 2011
  • Mathematica
    Table[7^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 9 x^2 + 6 x^3)/((1 - 7 x) (1 - x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
LinearRecurrence[{10,-24,22,-7},{1,6,45,334},20] (* Harvey P. Dale, Sep 16 2023 *)
  • PARI
    a(n)=7^n-n^2 \\ Charles R Greathouse IV, Oct 06 2014

Formula

G.f.: (1-4*x+9*x^2+6*x^3)/((1-7*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014
a(n) = 10*a(n-1) -24*a(n-2) +22*a(n-3) -7*a(n-4) for n>3. - Vincenzo Librandi, Oct 06 2014

A024090 8^n-n^2.

Original entry on oeis.org

1, 7, 60, 503, 4080, 32743, 262108, 2097103, 16777152, 134217647, 1073741724, 8589934471, 68719476592, 549755813719, 4398046510908, 35184372088607, 281474976710400, 2251799813684959, 18014398509481660
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. similar sequences listed in A024025.

Programs

  • Magma
    [8^n-n^2: n in [0..20]]; // Vincenzo Librandi, Jul 05 2011
  • Mathematica
    Table[8^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 10 x^2 + 7 x^3)/((1 - 8 x) (1 - x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
LinearRecurrence[{11,-27,25,-8},{1,7,60,503},30] (* Harvey P. Dale, Feb 13 2023 *)

Formula

G.f.: (1-4*x+10*x^2+7*x^3)/((1-8*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014
a(n) = 11*a(n-1) -27*a(n-2) +25*a(n-3) -8*a(n-4) for n>3. - Vincenzo Librandi, Oct 06 2014
a(n) = A001018(n) - A000290(n). - Michel Marcus, Oct 06 2014

A024103 a(n) = 9^n - n^2.

Original entry on oeis.org

1, 8, 77, 720, 6545, 59024, 531405, 4782920, 43046657, 387420408, 3486784301, 31381059488, 282429536337, 2541865828160, 22876792454765, 205891132094424, 1853020188851585, 16677181699666280, 150094635296998797
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A000290, A001019.
Cf. similar sequences listed in A024025.

Programs

  • Magma
    [9^n-n^2: n in [0..25]]; // Vincenzo Librandi, Jul 06 2011
  • Mathematica
    Table[9^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 11 x^2 + 8 x^3)/((1 - 9 x) (1 - x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)

Formula

G.f.: (1-4*x+11*x^2+8*x^3)/((1-9*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014
a(n) = 12*a(n-1) -30*a(n-2) +28*a(n-3) -9*a(n-4) for n>3. - Vincenzo Librandi, Oct 06 2014
a(n) = A001019(n) - A000290(n). - Michel Marcus, Oct 06 2014

A024116 a(n) = 10^n - n^2.

Original entry on oeis.org

1, 9, 96, 991, 9984, 99975, 999964, 9999951, 99999936, 999999919, 9999999900, 99999999879, 999999999856, 9999999999831, 99999999999804, 999999999999775, 9999999999999744, 99999999999999711, 999999999999999676
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. similar sequences listed in A024025.

Programs

  • Magma
    [10^n-n^2: n in [0..20]]; // Vincenzo Librandi, Jun 30 2011
  • Mathematica
    Table[10^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 12 x^2 + 9 x^3)/((1 - 10 x) (1-x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
LinearRecurrence[{13,-33,31,-10},{1,9,96,991},20] (* Harvey P. Dale, May 29 2021 *)

Formula

G.f.: (1-4*x+12*x^2+9*x^3)/((1-10*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014
a(n) = 13*a(n-1) -33*a(n-2) +31*a(n-3) -10*a(n-4) for n>3. - Vincenzo Librandi, Oct 06 2014
a(n) = A011557(n) - A000290(n). - Michel Marcus, Oct 06 2014

A024129 11^n-n^2.

Original entry on oeis.org

1, 10, 117, 1322, 14625, 161026, 1771525, 19487122, 214358817, 2357947610, 25937424501, 285311670490, 3138428376577, 34522712143762, 379749833583045, 4177248169415426, 45949729863571905, 505447028499293482
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. similar sequences listed in A024025.

Programs

  • Magma
    [11^n-n^2: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011
  • Mathematica
    Table[11^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 13 x^2 + 10 x^3)/((1 - 11 x) (1 - x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
LinearRecurrence[{14,-36,34,-11},{1,10,117,1322},20] (* Harvey P. Dale, Jul 03 2021 *)
  • PARI
    a(n)=11^n-n^2 \\ Charles R Greathouse IV, Jul 01 2011

Formula

G.f.: (1-4*x+13*x^2+10*x^3)/((1-11*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014

A024142 12^n-n^2.

Original entry on oeis.org

1, 11, 140, 1719, 20720, 248807, 2985948, 35831759, 429981632, 5159780271, 61917364124, 743008370567, 8916100448112, 106993205378903, 1283918464548668, 15407021574586143, 184884258895036160
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. similar sequences listed in A024025.

Programs

  • Magma
    [12^n-n^2: n in [0..20]]; // Vincenzo Librandi, Jul 01 2011
  • Mathematica
    Table[12^n - n^2, {n, 0, 25}] (* or *) CoefficientList[Series[(1 - 4 x + 14 x^2 + 11 x^3)/((1 - 12 x) (1 - x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 06 2014 *)
  • PARI
    a(n)=12^n-n^2 \\ Charles R Greathouse IV, Jul 01 2011

Formula

G.f.: (1-4*x+14*x^2+11*x^3)/((1-12*x)*(1-x)^3). - Vincenzo Librandi, Oct 06 2014
Showing 1-6 of 6 results.

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

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