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.

A010726 Period 2: repeat (6,10).

Original entry on oeis.org

6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10, 6, 10
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Comments

From Klaus Brockhaus, Dec 10 2009: (Start)
Interleaving of A010722 and A010692.
Also continued fraction expansion of 3 + 4*sqrt(15)/5.
Binomial transform of 6 followed by A122803 without initial terms 1,-2.
Inverse binomial transform of A171494. (End)

Links

Crossrefs

Equals 2*A010703. Cf. A010722 (all 6's sequence), A010692 (all 10's sequence), A122803 (powers of -2), A171494. - Klaus Brockhaus, Dec 10 2009

Programs

Formula

a(n) = -2*(-1)^n + 8. - Paolo P. Lava, Oct 27 2006
From Klaus Brockhaus, Dec 10 2009: (Start)
a(n) = a(n-2) for n > 1; a(0) = 6, a(1) = 10.
G.f.: 2*(3+5*x)/((1-x)*(1+x)). (End)

A171496 a(n) = 6*a(n-1) - 8*a(n-2) for n > 1; a(0) = 6, a(1) = 28.

Original entry on oeis.org

6, 28, 120, 496, 2016, 8128, 32640, 130816, 523776, 2096128, 8386560, 33550336, 134209536, 536854528, 2147450880, 8589869056, 34359607296, 137438691328, 549755289600, 2199022206976, 8796090925056, 35184367894528
Offset: 0

Views

Author

Klaus Brockhaus, Dec 10 2009

Keywords

Comments

Binomial transform of A171495; second binomial transform of A171494; third binomial transform of A010726.

Links

Crossrefs

Equals 2*A171499.
Cf. A171476, A006516, A010036, A171494, A171495, A010726, A171472, A171473.

Programs

  • Magma
    [8*4^n-2*2^n: n in [0..30]]; // Vincenzo Librandi, Jul 18 2011
  • Mathematica
    LinearRecurrence[{6,-8},{6,28},30] (* Harvey P. Dale, Dec 21 2014 *)
  • PARI
    {m=22; v=concat([6, 28], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-8*v[n-2]); v}

Formula

a(n) = 8*4^n - 2*2^n.
G.f.: 2*(3-4*x)/((1-2*x)*(1-4*x)).
a(n) = A171476(n+1) = A006516(n+2).
a(n+1) - a(n) = A010036(n+2).
a(n) = 4*a(n-1)+2^(n+1) (with a(0)=6). - Vincenzo Librandi, Dec 04 2010
E.g.f.: 2*exp(2*x)*(2*exp(2*x) - 1)*(2*exp(2*x) + 1). - Stefano Spezia, Dec 10 2021

A171495 a(n) = 3*a(n-1)+4 for n > 0; a(0) = 6.

Original entry on oeis.org

6, 22, 70, 214, 646, 1942, 5830, 17494, 52486, 157462, 472390, 1417174, 4251526, 12754582, 38263750, 114791254, 344373766, 1033121302, 3099363910, 9298091734, 27894275206, 83682825622, 251048476870, 753145430614, 2259436291846
Offset: 0

Views

Author

Klaus Brockhaus, Dec 10 2009

Keywords

Comments

Binomial transform of A171494; second binomial transform of A010726.
Inverse binomial transform of A171496.

Links

Crossrefs

Equals 2*A171498.
Cf. A010726 (repeat 6, 10), A171494, A171496.

Programs

  • Mathematica
    NestList[3#+4&,6,30] (* Harvey P. Dale, Aug 25 2019 *)
  • PARI
    {m=25; v=concat([6], vector(m-1)); for(n=2, m, v[n]=3*v[n-1]+4); v}

Formula

a(n) = 2*(4*3^n-1).
G.f.: 2*(3-x)/((1-x)*(1-3*x)).
Showing 1-3 of 3 results.

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

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