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.

A007162 Number of skeins with vertical symmetry.

Original entry on oeis.org

1, 1, 2, 7, 24, 96, 388, 1667, 7278, 32726, 149232, 692014, 3244182, 15374906, 73474008, 353835147, 1714967402, 8360511370, 40964207460, 201630767026, 996494168808, 4943036743112, 24601517883704, 122815436413582, 614828204108840
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

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

Links

Crossrefs

Cf. A007161, A007165.

Formula

a(n) = coefficient of x^(2n+1) in x + H(x) * C(x) where H(x) = Sum_{k=1..infinity} A007165(k) * x^(2k) and C(x) = Sum_{k=0..infinity} A007161(k) * x^(2k+1). - Sean A. Irvine, Nov 06 2017

Extensions

More terms from Sean A. Irvine, Nov 06 2017

A294728 Number of Q graphs with 2*n vertices symmetrical about a distinguished edge.

Original entry on oeis.org

0, 0, 0, 1, 1, 6, 7, 37, 47, 242, 324, 1658, 2300, 11764, 16741, 85741, 124383, 638250, 939880, 4832446, 7202214, 37101556, 55842670, 288180066, 437325262, 2260516372, 3454370352, 17881862308, 27489383818, 142491830992, 220185726817
Offset: 1

Views

Author

Sean A. Irvine, Nov 07 2017

Keywords

Links

Crossrefs

Cf. A003168, A007165.

Formula

G.f.: H(x) * (B(x^2) - x^2) where H(x) is the g.f. for A007165 and B(x) is the g.f. for A003168.

A007164 Number of P-graphs with 2n edges.

Original entry on oeis.org

1, 2, 7, 31, 167, 999, 6495, 44619, 319463, 2356406, 17775821, 136405506, 1060866006, 8339982193, 66147792753, 528559162227, 4250413757583, 34368723106860, 279254390054538, 2278795583070154, 18667432144042678, 153452484745198722
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • R. C. Read, On the enumeration of a class of plane multigraphs, Aequat. Math., 31 (1986), 47-63.
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Crossrefs

Cf. A003169, A007163, A007165.

Formula

a(n) = (A003169(n) + 2 * A007165(n) + A007163(n)) / 4. - Sean A. Irvine, Nov 06 2017

Extensions

a(5), a(9), a(10) corrected and more terms from Sean A. Irvine, Nov 06 2017

A007171 Number of Q-graphs with 2n edges.

Original entry on oeis.org

1, 2, 4, 16, 89, 579, 3989, 28630, 210865, 1584308, 12091902, 93483120, 730503054, 5760438853, 45780146521, 366304396662, 2948412461685, 23857049238752, 193944769559906, 1583294537879106, 12974430494985262, 106685110047676402
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

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

Links

Crossrefs

Cf. A003169, A007165, A007170.

Formula

a(1) = 1, a(n) = A007170(n) + (A003169(n-1) + A007165(n-1)) / 2. - Sean A. Irvine, Nov 07 2017

Extensions

a(9) corrected and more terms from Sean A. Irvine, Nov 07 2017
Showing 1-4 of 4 results.

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

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