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 1-4 of 4 results.

A292002 Number of (undirected) paths in the n-Apollonian network.

Original entry on oeis.org

30, 1017, 1417992, 1475602431690, 887899295279284798114284, 580352523353299355481324176693737926736684735143
Offset: 1

Views

Author

Eric W. Weisstein, Sep 07 2017

Keywords

Comments

a(7) has 96 decimal digits and a(8) has 191 decimal digits. - Andrew Howroyd, Jun 09 2025

Links

Crossrefs

Cf. A302718, A307549.

Extensions

a(4) onwards from Andrew Howroyd, Jun 09 2025

A302718 Number of cycles in the n-Apollonian network.

Original entry on oeis.org

7, 119, 27850, 2635637428, 40538274896917926642, 18915440603912727411772352213199539580794, 4811072124719412065599148626063536230790419188877913496386013668865001860521888965
Offset: 1

Views

Author

Eric W. Weisstein, Apr 14 2018

Keywords

Comments

a(8) has 165 decimal digits and a(9) has 331 decimal digits. - Andrew Howroyd, Sep 09 2019

Links

Crossrefs

Cf. A292002, A301650, A307549.

Programs

  • PARI
    P(c,d)={[2*d^3 + 7*d^2 + (6*c + 2)*d + 2*c, 3*d^2 + 5*d + (c + 1)]}
R(c,d)={16*d^3 + (9*c + 51)*d^2 + (30*c + 27)*d + (3*c^2 + 9*c + 4)}
a(n)={my(s=1, c=0, d=0); for(i=1, n, s = 3*s + R(c,d); [c,d]=P(c,d)); s} \\ Andrew Howroyd, Sep 10 2019

Extensions

a(5)-a(7) from Andrew Howroyd, Sep 09 2019

A301650 Number of longest cycles in the n-Apollonian network.

Original entry on oeis.org

3, 12, 162, 354294, 1694577218886, 38766491335360039793593446, 20288351481136358057581328834353447021191164711091366
Offset: 1

Views

Author

Eric W. Weisstein, Mar 25 2018

Keywords

Comments

From Andrew Howroyd, Sep 09 2019: (Start)
a(8) has 106 decimal digits and a(9) has 213 decimal digits.
The circumference or length of the longest cycle is given by 7*2^(n-2) for n > 1. For n = 1, the circumference is 4. (End)

Links

Crossrefs

Cf. A292002, A302718, A307549.

Programs

  • PARI
    P(c,d,x)={[d^2 + 6*c*d + 2*d^3 + 2*x*(c + 3*d^2) + 2*x^2*d, c + d + 3*d^2 + 4*x*d + x^2]}
R(c,d,x)={4*d^3 + 9*c*d^2 + 3*d^2 + 6*c*d + 3*c^2 + 6*x*(2*d^3 + 3*d^2 + 4*c*d) + 3*x^2*(10*d^2 + 3*d + 3*c) + x^3*(18*d + 1) + 3*x^4}
a(n)={my(s=x^3, c=0, d=0); for(i=1, n, s = 3*s + R(c,d,x); [c,d]=P(c,d,x)); pollead(s)} \\ Andrew Howroyd, Sep 10 2019

Extensions

a(5)-a(7) from Andrew Howroyd, Sep 09 2019

A307457 Longest path length in the n-Apollonian network.

Original entry on oeis.org

3, 6, 14, 30, 62, 126, 254, 510, 1022, 2046, 4094, 8190, 16382, 32766, 65534, 131070, 262142, 524286, 1048574, 2097150, 4194302, 8388606, 16777214, 33554430, 67108862, 134217726, 268435454, 536870910, 1073741822, 2147483646, 4294967294, 8589934590
Offset: 1

Views

Author

Eric W. Weisstein, Apr 08 2019

Keywords

Links

Crossrefs

Essentially the same as A000918 shifted, and A095121.
Cf. A307549.

Formula

a(n) = 2^(n+1) - 2 = A000918(n+1) for n > 1. - Andrew Howroyd, Jun 09 2025

Extensions

a(5) onwards from Andrew Howroyd, Jun 09 2025
Showing 1-4 of 4 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.