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.

A372892 Total number of unlabeled simple maps on the sphere with n vertices.

Original entry on oeis.org

1, 1, 2, 6, 25, 179, 2014, 31178, 580555, 12046072, 267836680, 6258809085, 151983244000, 3807081193879
Offset: 1

Views

Author

Eric W. Weisstein, May 19 2024

Keywords

Comments

Computed by Brendan McKay.
a(n) is the same as the total number of distinct spherical drawings of connected graphs with n vertices.

Links

Crossrefs

Row sums of A384963, column sums of A384850.
Cf. A372853 (uniquely embeddable connected graphs).
Cf. A372854 (largest numbers of planar embeddings for connected graphs).
Cf. A006395 (with n edges), A384965 (sensed version).

Extensions

a(14) added by Andrew Howroyd, Jun 13 2025

A372854 Maximum numbers of planar embeddings for connected planar graphs on n vertices.

Original entry on oeis.org

1, 1, 1, 1, 2, 6, 24, 80, 240, 1080, 3780, 13440
Offset: 1

Views

Author

Eric W. Weisstein, May 15 2024

Keywords

Comments

Computed by Stan Wagon up to n=7 and Brendan McKay up to n=12.

Links

Crossrefs

Cf. A372853 (uniquely embeddable planar connected graphs).

A378672 Numbers of uniquely embeddable trees on n vertices.

Original entry on oeis.org

1, 1, 1, 2, 3, 6, 10, 19, 31, 57, 95, 161, 262, 435, 683, 1081, 1665, 2545, 3800, 5658, 8232, 11935, 17012, 24074, 33606, 46698, 63994, 87281, 117797, 158121, 210240, 278389, 365267, 477416, 619278, 799962, 1026370, 1312419, 1667131, 2111086
Offset: 1

Views

Author

Eric W. Weisstein, Dec 03 2024

Keywords

Links

Crossrefs

Cf. A378673 (not uniquely embeddable trees).
Cf. A372853 (uniquely embeddable planar connected graphs).
Cf. A000055 (trees), A003238.

Programs

  • PARI
    \\ G(n) is A003238 as g.f.
G(n) = {my(v=vector(n)); v[1]=1; for(i=2, n, v[i]=sumdiv(i-1, d, v[d])); x*Ser(v)}
seq(n) = {my(g=G(n-1)); Vec(x + ((1 - x)*g^2 + (1 + x)*subst(g,x,x^2))/2 + x*(g^3 - 3*g*subst(g,x,x^2) + 2*subst(g,x,x^3))/6)} \\ Andrew Howroyd, Jun 08 2025

Formula

a(n) = A000055(n) - A378673(n).
G.f.: x + ((1 - x)*g(x)^2 + (1 + x)*g(x^2))/2 + x*(g(x)^3 - 3*g(x)*g(x^2) + 2*g(x^3))/6, where g(x) is the g.f. of A003238. - Andrew Howroyd, Jun 08 2025

Extensions

a(13) onwards from Andrew Howroyd, Jun 08 2025

A378673 Numbers of not uniquely embeddable trees on n vertices.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 4, 16, 49, 140, 390, 1039, 2724, 7058, 18239, 46964, 121322, 314155, 817407, 2136273, 5611821, 14811062, 39275823, 104603284, 279746752, 751001466, 2023355751, 5469448788, 14830713681, 40330618790, 109972131832, 300628497213, 823779154305, 2262365724468
Offset: 1

Views

Author

Eric W. Weisstein, Dec 03 2024

Keywords

Links

Crossrefs

Cf. A378672 (uniquely embeddable trees).
Cf. A372853 (uniquely embeddable planar connected graphs).
Cf. A000055 (trees).

Formula

a(n) = A000055(n) - A378672(n).

Extensions

a(13) onwards from Andrew Howroyd, Jun 08 2025
Showing 1-4 of 4 results.

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

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