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 1-2 of 2 results.

A176414 Expansion of (7+8*x)/(1+2*x).

Original entry on oeis.org

7, -6, 12, -24, 48, -96, 192, -384, 768, -1536, 3072, -6144, 12288, -24576, 49152, -98304, 196608, -393216, 786432, -1572864, 3145728, -6291456, 12582912, -25165824, 50331648, -100663296, 201326592, -402653184, 805306368
Offset: 0

Views

Author

Klaus Brockhaus, Apr 17 2010

Keywords

Comments

Inverse binomial transform of A176415.

Links

Crossrefs

Cf. A176415, A110164 (essentially the same), A122803.

Programs

  • Mathematica
    Join[{7},NestList[-2#&,-6,40]] (* Harvey P. Dale, Jun 20 2020 *)
  • PARI
    {for(n=0, 29, print1(polcoeff((7+8*x)/(1+2*x)+x*O(x^n), n), ", "))}
  • PARI
    A176414(n)=3*(-2)^n+!n*4 \\ M. F. Hasler, Apr 19 2015

Formula

a(n) = A110164(n+2) for n > 0.
a(n) = 3*(-2)^n = 3*A122803(n+1) for n > 0; a(0) = 7.
a(n) = -2*a(n-1) for n > 1; a(0) = 7, a(1) = -6.
a(n) = (-1)^n*A132477(n) = (-1)^n*A122391(n+3), n>1.
a(n) = (-1)^n*A111286(n+2) = (-1)^n*A098011(n+4) = (-1)^n*A091629(n) = (-1)^n*A087009(n+3) = (-1)^n*A082505(n+1) = (-1)^n*A042950(n+1) = (-1)^n*A007283(n) = (-1)^n*A003945(n+1), n>0. - R. J. Mathar, Dec 10 2010
E.g.f.: 4 + 3*exp(-2*x). - Alejandro J. Becerra Jr., Feb 15 2021

Extensions

Edited by M. F. Hasler, Apr 19 2015

A132476 A007318^(-1) * [3*A007318^2 - 2*A000012].

Original entry on oeis.org

1, 3, 1, 3, 8, 1, 3, 7, 13, 1, 3, 14, 12, 18, 1, 3, 13, 38, 18, 23, 1, 3, 20, 35, 80, 25, 28, 1, 3, 19, 75, 75, 145, 33, 33, 1, 3, 26, 70, 210, 140, 238, 42, 38, 1, 3, 25, 124, 196, 490, 238, 364, 52, 43, 1
Offset: 0

Views

Author

Gary W. Adamson, Aug 22 2007

Keywords

Comments

Row sums = A132477: (1, 4, 12, 24, 48, 96, 192, ...).

Examples

			First few rows of the triangle:
  1;
  3,  1;
  3,  8,  1;
  3,  7, 13,  1;
  3, 14, 12, 18,  1;
  3, 13, 38, 18, 23,  1;
  3, 20, 35, 80, 25, 28,  1;
  ...

Crossrefs

Cf. A007318, A000012, A132477.

Formula

Inverse binomial transform of [3*A007318 - 2*A000012], as infinite lower triangular matrices.
Showing 1-2 of 2 results.

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