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 1-6 of 6 results.

A006389 Number of unsensed planar maps with n edges and without faces of degree 1.

Original entry on oeis.org

1, 1, 2, 6, 18, 68, 313, 1592, 9187, 57451, 384450, 2703970, 19769311
Offset: 0

Views

Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A006385, A006388 (sensed), A379433 (rooted).

Extensions

a(8)-a(12) from Sean A. Irvine, Mar 28 2017
a(0)=1 prepended by Andrew Howroyd, Jan 16 2025

A379433 Number of rooted planar maps with n edges and without faces of degree 1.

Original entry on oeis.org

1, 1, 3, 16, 96, 624, 4304, 31056, 232128, 1784752, 14043312, 112648848, 918456608, 7593649392, 63546379152, 537427956688, 4587713701248, 39488179213872, 342414691125104, 2989022121125136, 26249475365186016, 231786459869636464, 2056950693208881744
Offset: 0

Views

Author

Andrew Howroyd, Jan 14 2025

Keywords

Crossrefs

Cf. A000168, A006388 (sensed), A006389 (unsensed), A379434, A379435.

Programs

  • PARI
    seq(n)={my(z=x/(1 + x)^2, g=(-1 + 18*z + sqrt(1-12*z + O(x^(n+3)))^3) / (54*z^2)); Vec(x + g*(1-x)/(1+x))}

Formula

G.f.: x + G(x/(1 + x)^2)*(1 - x)/(1 + x) where G(x) is the g.f. of A000168.

A380365 Number of sensed combinatorial maps with n edges and without faces of degree 1.

Original entry on oeis.org

1, 1, 3, 11, 50, 365, 3782, 47935, 718202, 12245679, 233541489, 4920828395, 113495838798, 2843930973805, 76932818058660, 2234631397864123, 69368177318863458, 2291843543825994905, 80296746074069588380, 2973657775519950500203, 116065360915389313936460
Offset: 0

Views

Author

Andrew Howroyd, Jan 28 2025

Keywords

Crossrefs

Cf. A006388 (planar), A170946, A380364 (rooted), A380366 (unsensed).

Programs

  • PARI
    InvEulerT(v)={dirdiv(Vec(log(1+x*Ser(v)),-#v), vector(#v,n,1/n))}
    b(k,r)={if(k%2, if(r%2, 0, my(j=r/2); k^j*(2*j)!/(j!*2^j)), sum(j=0, r\2, binomial(r, 2*j)*k^j*(2*j)!/(j!*2^j)))}
    C(k,r)={sum(i=0, r, (-1)^i/i!/k^i)}
    S(n,k)={sum(r=0, 2*n\k, if(k*r%2==0, x^(k*r/2)*b(k,r)*C(k,r)), O(x*x^n))}
    seq(n)={concat([1], InvEulerT(Vec(-1 + prod(k=1, 2*n, S(n,k)))))}

A006392 Number of sensed planar maps with n edges and without faces of degree 1 or 2.

Original entry on oeis.org

1, 0, 1, 4, 9, 34, 161, 830, 4779, 29092, 184510, 1208178, 8116922
Offset: 0

Views

Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A006384, A006388, A006393 (unsensed), A379434 (rooted).

Extensions

a(8)-a(12) from Sean A. Irvine, Mar 29 2017
a(0)-a(1) prepended by Andrew Howroyd, Jan 16 2025

A006396 Number of sensed planar maps with n edges and without faces or vertices of degree 1.

Original entry on oeis.org

1, 0, 1, 2, 4, 10, 36, 132, 616, 3060, 16207, 88990, 503816
Offset: 0

Views

Author

Keywords

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A006384, A006388, A006397 (unsensed), A379435 (rooted).

Extensions

a(9)-a(12) from Sean A. Irvine, Mar 28 2017
a(0)-a(2) prepended by Andrew Howroyd, Jan 16 2025

A006400 Number of sensed simple planar maps with n edges and without vertices of degree 1.

Original entry on oeis.org

1, 0, 0, 1, 1, 2, 5, 11, 33, 117, 431, 1755, 7485
Offset: 0

Views

Author

Keywords

Comments

A simple planar map is a planar map without loops or parallel edges. - Andrew Howroyd, Jan 16 2025

References

  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A006384, A006388, A006394, A006401 (unsensed), A379436 (rooted).

Extensions

a(11) and a(12) from Sean A. Irvine, Mar 30 2017
a(0)-a(2) prepended by Andrew Howroyd, Jan 14 2025
Showing 1-6 of 6 results.