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.

A191467 9^n - 7^n.

Original entry on oeis.org

0, 2, 32, 386, 4160, 42242, 413792, 3959426, 37281920, 347066882, 3204309152, 29403732866, 268588249280, 2444976817922, 22198569382112, 201143570584706, 1819787258282240, 16444551185679362, 148466221699088672, 1339452822487618946
Offset: 0

Views

Author

Vincenzo Librandi, Jun 03 2011

Keywords

Links

Crossrefs

Cf. A118004, A016178, A016185, A059410, A139745, A191467.

Programs

  • Magma
    [9^n - 7^n: n in [0..20]]:
  • Mathematica
    Table[9^n-7^n,{n,0,20}] (* or *) LinearRecurrence[{16,-63},{0,2},20] (* Harvey P. Dale, Jun 21 2014 *)
CoefficientList[Series[2 x/((1 - 7 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *)
  • PARI
    a(n)=9^n-7^n \\ Charles R Greathouse IV, Jun 08 2011

Formula

a(n) = 16*a(n-1) - 63*a(n-2).
G.f.: 2*x/((1-7*x)*(1-9*x)). - Vincenzo Librandi, Oct 05 2014
a(n+1) = 2*A016178(n). - Vincenzo Librandi, Oct 05 2014

A016183 Expansion of g.f. 1/((1-7*x)*(1-11*x)).

Original entry on oeis.org

1, 18, 247, 3060, 36061, 413478, 4665907, 52148520, 579398521, 6413737338, 70833585967, 781146772380, 8606455783381, 94767902627598, 1043125151976427, 11479124233250640, 126303599496326641
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Links

Crossrefs

Cf. A139745.

Formula

a(n) = (11^(n+1) - 7^(n+1))/4. - Al Hakanson (hawkuu(AT)gmail.com), Dec 31 2008; adapted to offset by Michel Marcus, Mar 09 2025
a(n) = 18*a(n-1) - 77*a(n-2). - Philippe Deléham, Jan 01 2009
a(n) = 11*a(n-1) + 7^n, a(0)=1. - Vincenzo Librandi, Feb 09 2011
From Elmo R. Oliveira, Mar 09 2025: (Start)
E.g.f.: exp(7*x)*(11*exp(4*x) - 7)/4.
a(n) = A139745(n+1)/4. (End)

A248341 a(n) = 10^n - 7^n.

Original entry on oeis.org

0, 3, 51, 657, 7599, 83193, 882351, 9176457, 94235199, 959646393, 9717524751, 98022673257, 986158712799, 9903110989593, 99321776927151, 995252438490057, 9966767069430399, 99767369486012793, 998371586402089551, 9988601104814626857
Offset: 0

Views

Author

Vincenzo Librandi, Oct 05 2014

Keywords

Links

Crossrefs

Cf. sequences of the form k^n-7^n: A016177 (k=8), A191467 (k=9), this sequence(k=10), A139745 (k=11).
Cf. A000420, A011557, A016181.

Programs

  • Magma
    [10^n-7^n: n in [0..30]];
  • Mathematica
    Table[10^n - 7^n, {n, 0, 25}] (* or *) CoefficientList[Series[3 x/((1 - 7 x) (1 - 10 x)), {x, 0, 30}], x]
LinearRecurrence[{17,-70},{0,3},20] (* Harvey P. Dale, Dec 18 2020 *)

Formula

G.f.: 3*x/((1-7*x)*(1-10*x)).
a(n) = 17*a(n-1) - 70*a(n-2).
a(n) = A011557(n) - A000420(n).
a(n+1) = 3*A016181(n).
E.g.f.: 2*exp(17*x/2)*sinh(3*x/2). - Elmo R. Oliveira, Apr 01 2025
Showing 1-3 of 3 results.

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

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