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.

Previous Showing 11-16 of 16 results.

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.

A004040 Inversion of A000257.

Original entry on oeis.org

1, 2, 6, 23, 103, 512, 2740, 15485, 91245, 555662, 3475090, 22214707, 144640291, 956560748, 6411521056, 43478151737, 297864793993, 2059159989914, 14350039389022, 100726680316559, 711630547589023, 5057282786190872, 36132861123763276, 259423620328055093, 1870954187618001253
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

Crossrefs

Cf. A000257.
Essentially the same as A022558.

Programs

  • PARI
    x='x+O('x^66); Vec( -1 + 32*x/(1+20*x-8*x^2-(1-8*x)^(3/2)) ) \\ Joerg Arndt, May 04 2013

Formula

Invert: define b by 1+Sum a(n)x^n = 1/(1 - Sum b(n)x^n).

Extensions

More terms from Joerg Arndt, May 04 2013

A248900 Number of permutations of [n] avoiding patterns 2431 and 54321.

Original entry on oeis.org

1, 1, 2, 6, 23, 102, 492, 2492, 13003, 69172, 372963, 2031174, 11148948, 61588814, 342068774, 1908740089, 10694374242, 60137305751, 339276548456, 1919787554118, 10892575241125, 61957028188350, 353224194632459, 2018076850631391, 11552829351121139, 66259093178740462
Offset: 0

Views

Author

Nathaniel Shar, Mar 06 2015

Keywords

Examples

			a(4) = 23 because all permutations of length 4 except 2431 lie in this set.

Links

Crossrefs

Cf. A022558, A047889.

A284712 Number of indecomposable permutations avoiding the pattern 4321.

Original entry on oeis.org

1, 1, 3, 12, 56, 289, 1603, 9391, 57437, 363773, 2371551, 15842850, 108070370, 750655459, 5297314241, 37909476912, 274693258884, 2012767854337, 14897269924571, 111269729060260, 838012360130944, 6359434553977763, 48597188639038769, 373757879279966501
Offset: 1

Views

Author

N. J. A. Sloane, Apr 02 2017

Keywords

Links

Crossrefs

Cf. A005802, A022558.

Programs

  • Mathematica
    Rest[CoefficientList[Series[1 - 6*x^2/(1 + 5*x - (1-9*x)^(3/4) * (1-x)^(1/4) * HypergeometricPFQ[{-1/4, 3/4}, {1}, 64*x/((x-1)*(1-9*x)^3)]), {x, 0, 30}], x]] (* Vaclav Kotesovec, Apr 03 2017 *)

Formula

a(n) ~ c * 3^(2*n) / n^4, where c = 2.102569600767282153... . - Vaclav Kotesovec, Apr 03 2017

Extensions

More terms from Vaclav Kotesovec, Apr 03 2017

A239298 Words of length n over the alphabet {0,...,n-1} that are 1342-avoiding.

Original entry on oeis.org

1, 1, 4, 27, 255, 3028, 41972, 647034, 10760307, 189317370, 3478597980
Offset: 0

Views

Author

Chad Brewbaker, Mar 14 2014

Keywords

Crossrefs

The permutation analog is A022558.
Cf. A000312.

Extensions

a(8)-a(10) from Giovanni Resta, Mar 14 2014

A248426 Number of permutations of length n avoiding the pattern 1342 and with 1 appearing before n.

Original entry on oeis.org

1, 3, 11, 46, 211, 1038, 5400, 29425, 166767, 977637, 5901299, 36538483, 231286924, 1492482109, 9793849702, 65217085321, 439887071563, 3000650380603, 20673092451143, 143687057466690, 1006538694994567, 7100409431126274, 50404258628152846, 359845398688215262
Offset: 2

Views

Author

Nathaniel Shar, Oct 06 2014

Keywords

Examples

			For n=4 the 11 permutations are: 1234, 1243, 1324, 1423, 1432, 2134, 2143, 2314, 3124, 3142, 3214.

Crossrefs

Cf. A022558.

Formula

G.f.: (-1 + sqrt((8*x-1)*sqrt(1-8*x) - 136*x^2 + 20*x + 1)/sqrt((8*x-1)*sqrt(1-8*x) - 8*x^2 + 20*x + 1))*((8*x-1)*sqrt(1-8*x) - 8*x^2 - 12*x + 1)/(64*x).
Previous Showing 11-16 of 16 results.

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

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