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.

A077265 Number of cycles in the n-th order prism graph.

Original entry on oeis.org

14, 28, 52, 94, 170, 312, 584, 1114, 2158, 4228, 8348, 16566, 32978, 65776, 131344, 262450, 524630, 1048956, 2097572, 4194766, 8389114, 16777768, 33555032, 67109514, 134218430, 268436212, 536871724, 1073742694, 2147484578, 4294968288, 8589935648, 17179870306
Offset: 3

Views

Author

Eric W. Weisstein, Nov 01 2002

Keywords

Comments

Also the number of cycles in the n-th order web graph. - Eric W. Weisstein, Dec 17 2013
Also the number of minimal edge cuts in the n-dipyramidal graph. - Eric W. Weisstein, Oct 30 2024
A subsequence of A290699.

Links

Crossrefs

Cf. A077263, A260699.
Cf. A000079, A002378, A132109.

Programs

Formula

a(n) = 2^n+n*(n-1). - Eric W. Weisstein, Dec 16 2013
a(n) = 5*a(n-1)-9*a(n-2)+7*a(n-3)-2*a(n-4). - Colin Barker, May 06 2014
G.f.: -2*x^3*(6*x^3-19*x^2+21*x-7) / ((x-1)^3*(2*x-1)). - Colin Barker, May 06 2014
a(n) = A000079(n) + A002378(n-1). - Wesley Ivan Hurt, May 07 2014
a(n) = 2*A132109(n-1). - R. J. Mathar, May 23 2016

Extensions

More terms from Eric W. Weisstein, Dec 16 2013

A132108 Triangle T(n,k) = binomial(n,k)+n-k read by rows.

Original entry on oeis.org

1, 2, 1, 3, 3, 1, 4, 5, 4, 1, 5, 7, 8, 5, 1, 6, 9, 13, 12, 6, 1, 7, 11, 19, 23, 17, 7, 1, 8, 13, 26, 39, 38, 23, 8, 1, 9, 15, 34, 61, 74, 59, 30, 9, 1, 10, 17, 43, 90, 131, 130, 87, 38, 10, 1
Offset: 0

Views

Author

Gary W. Adamson, Aug 09 2007

Keywords

Examples

			First few rows of the triangle are:
1;
2, 1;
3, 3, 1;
4, 5, 4, 1;
5, 7, 8, 5, 1;
6, 9, 13, 12, 6, 1;
7, 11, 19, 23, 17, 7, 1;
...

Links

Crossrefs

Cf. A007318, A002024, A002260, A132109 (row sums).

Programs

  • Magma
    /* As triangle: */ [[Binomial(n,k)+n-k: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, May 23 2016
  • Mathematica
    Table[Binomial[n,k]+n-k,{n,0,10},{k,0,n}]//Flatten (* Harvey P. Dale, Mar 08 2018 *)

Formula

T(n,k) = A007318(n,k) + A002024(n,k) - A002260(n,k).

A290699 a(n) = 2^n - n + n^2.

Original entry on oeis.org

0, 2, 6, 14, 28, 52, 94, 170, 312, 584, 1114, 2158, 4228, 8348, 16566, 32978, 65776, 131344, 262450, 524630, 1048956, 2097572, 4194766, 8389114, 16777768, 33555032, 67109514, 134218430, 268436212, 536871724, 1073742694, 2147484578, 4294968288, 8589935648, 17179870306
Offset: 0

Views

Author

Eric W. Weisstein, Aug 09 2017

Keywords

Comments

Number of minimal edge covers in the n-book graph.

Links

Crossrefs

Cf. A132109.
A077265 is a subsequence.

Programs

  • Mathematica
    Table[2^n - n + n^2, {n, 20}]
LinearRecurrence[{5, -9, 7, -2}, {2, 6, 14, 28}, 20]
CoefficientList[Series[-((2 (-1 + 2 x - x^2 + x^3))/((-1 + x)^3 (-1 + 2 x))), {x, 0, 20}], x]

Formula

a(n) = 2*A132109(n-1).
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4).
G.f.: -((2 x (-1 + 2 x - x^2 + x^3))/((-1 + x)^3 (-1 + 2 x))).

Extensions

Added a(0)=0. - N. J. A. Sloane, May 25 2019
Showing 1-3 of 3 results.

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

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