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.

A034270 f(n,n+3) where f is given in A034261.

Original entry on oeis.org

0, 1, 13, 99, 605, 3289, 16653, 80444, 375972, 1715130, 7681586, 33913385, 148018455, 640049865, 2746422525, 11708971560, 49647131160, 209523969630, 880668859590, 3688555690950, 15401089588794, 64128925255626, 266376231244178, 1104047701891624, 4566956385797400
Offset: 0

Views

Author

Clark Kimberling

Keywords

Links

Crossrefs

Cf. A000302, A034261, A249521.

Programs

  • Magma
    [n*(n^2+4*n+1)*Binomial(2*n+3, n)/((n+4)*(n+5)): n in [0..25]]; // Vincenzo Librandi, May 04 2013
  • Mathematica
    Table[n*(n^2+4*n+1)*Binomial[2*n+3,n]/((n+4)*(n+5)),{n,0,20}] (* Vaclav Kotesovec, Oct 27 2012 *)
  • PARI
    a(n)=n*(n^2+4*n+1)*binomial(2*n+3,n)/((n+4)*(n+5)); \\ Joerg Arndt, May 04 2013

Formula

a(n) ~ c*sqrt(n)*4^n, with c = 8/sqrt(Pi) = 2*A249521. - Stefano Spezia, Oct 19 2023

Extensions

Corrected and extended by N. J. A. Sloane, Apr 21 2000

A249539 Decimal expansion of 12/sqrt(Pi), the average perimeter of a random Gaussian triangle in three dimensions.

Original entry on oeis.org

6, 7, 7, 0, 2, 7, 5, 0, 0, 2, 5, 7, 3, 0, 7, 5, 4, 4, 3, 3, 7, 6, 9, 5, 3, 4, 1, 8, 7, 2, 9, 2, 7, 1, 0, 3, 0, 1, 2, 8, 6, 0, 7, 5, 5, 1, 9, 4, 7, 9, 8, 6, 2, 8, 2, 1, 2, 9, 0, 2, 8, 6, 6, 0, 5, 2, 7, 7, 0, 9, 6, 2, 1, 2, 9, 7, 9, 2, 0, 9, 7, 3, 8, 4, 0, 9, 2, 3, 9, 2, 2, 4, 2, 5, 2, 8, 8, 3, 6, 1, 3, 1, 6, 3, 4
Offset: 1

Views

Author

Jean-François Alcover, Oct 31 2014

Keywords

Examples

			6.770275002573075443376953418729271030128607551947986282129...

Links

Crossrefs

Cf. A102519, A102520, A102558, A102559, A249521 (average side length in three dimensions), A249538 (average perimeter in two dimensions).

Programs

A249522 Decimal expansion of the expected product of two sides of a random Gaussian triangle in three dimensions.

Original entry on oeis.org

5, 3, 0, 7, 9, 7, 3, 3, 7, 2, 5, 3, 0, 7, 5, 2, 2, 9, 7, 0, 6, 7, 9, 5, 8, 9, 8, 9, 8, 7, 7, 8, 1, 6, 6, 4, 8, 3, 8, 4, 3, 1, 8, 8, 8, 2, 1, 9, 9, 8, 4, 3, 9, 1, 6, 7, 9, 6, 1, 9, 6, 1, 2, 1, 7, 4, 6, 1, 8, 1, 8, 2, 0, 8, 1, 5, 6, 1, 8, 7, 6, 9, 0, 4, 2, 2, 8, 0, 1, 7, 2, 9, 3, 9, 0, 2, 5, 3, 3, 5, 2, 4, 6
Offset: 1

Views

Author

Jean-François Alcover, Oct 31 2014

Keywords

Examples

			5.3079733725307522970679589898778166483843188821998439167961...

Links

Crossrefs

Cf. A102519, A102520, A102556, A102557, A102558, A102559, A249491, A249521.

Programs

  • Mathematica
    p = 2 + 6*Sqrt[3]/Pi; RealDigits[p, 10, 104] // First

Formula

p = 2 + 6*sqrt(3)/Pi.
Showing 1-3 of 3 results.

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

Content is available under The OEIS End-User License Agreement.