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.

A006388 Number of sensed planar maps with n edges and without faces of degree 1.

Original entry on oeis.org

1, 1, 2, 6, 18, 74, 393, 2282, 14700, 99614, 703519, 5123598, 38279496
Offset: 0

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Author

Keywords

References

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

Crossrefs

Cf. A006384, A006389 (unsensed), A379433 (rooted).

Extensions

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

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

A379434 Number of rooted planar maps with n edges and without faces of degree 1 or 2.

Original entry on oeis.org

1, 0, 2, 9, 47, 278, 1720, 11175, 75149, 519852
Offset: 0

Views

Author

Andrew Howroyd, Jan 14 2025

Keywords

Crossrefs

Cf. A000168, A006392 (sensed), A006393 (unsensed), A379433.

A379435 Number of rooted planar maps with n edges and without faces or vertices of degree 1.

Original entry on oeis.org

1, 0, 1, 2, 10, 52, 281, 1570, 9022, 53084, 318634, 1945396, 12052532, 75624616, 479814937, 3074251682, 19869323638, 129420288076, 848897059790, 5603350613308, 37198680816844, 248241480270680, 1664546969372554, 11210468046615412, 75806810042727980, 514537522249147672
Offset: 0

Views

Author

Andrew Howroyd, Jan 14 2025

Keywords

Crossrefs

Cf. A000168, A006396 (sensed), A006397 (unsensed), A379433.

Programs

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

Formula

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

A380364 Number of rooted combinatorial maps with n edges and without faces of degree 1.

Original entry on oeis.org

1, 1, 4, 30, 284, 3240, 43282, 662760, 11446844, 220193310, 4669558564, 108251161920, 2723857695362, 73941952968000, 2154117314613604, 67038931862069790, 2219781607638887804, 77922680046440538600, 2890682855602209593362, 112998995448368143038120, 4642614436461699746566364
Offset: 0

Views

Author

Andrew Howroyd, Jan 28 2025

Keywords

Crossrefs

Cf. A379433 (planar), A380365 (sensed), A380366 (unsensed).

Programs

  • PARI
    seq(n)={my(A=O(x^(2*n+1)), g=serconvol(exp(x^2/2 + A),exp(-x + A)/(1-x))); Vec(substpol(1 + x*deriv(log(serlaplace(g))), x^2, x))}

A379436 Number of rooted simple planar maps without vertices of degree 1.

Original entry on oeis.org

1, 0, 0, 1, 1, 6, 22, 92, 395, 1753
Offset: 0

Views

Author

Andrew Howroyd, Jan 14 2025

Keywords

Comments

A simple planar map is without loops or parallel edges.

Crossrefs

Cf. A006400 (sensed), A006401 (unsensed), A022558 (rooted simple planar maps), A379433.
Showing 1-6 of 6 results.