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 21-30 of 30 results.

A039625 Number of planar simply-connected mono-q-polyhexes for q=5.

Original entry on oeis.org

1, 1, 4, 15, 69, 329, 1635, 8208
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, Studies of some chemically relevant polygonal system mono-q-polyhexes, ACH Models in Chem., 133 (3) (1996), 277-298.

Crossrefs

Cf. A018190.

A126026 Conjectured upper bound on area of the convex hull of any edge-to-edge connected system of regular unit hexagons (n-polyhexes).

Original entry on oeis.org

0, 1, 2, 4, 5, 8, 10, 13, 17, 20, 24, 28, 33, 38, 43, 49, 55, 61, 68, 75, 82, 90, 97, 106, 114, 123, 133, 142, 152, 162, 173, 184, 195, 207, 219, 231, 244, 257, 270, 284, 297, 312, 326, 341, 357, 372, 388, 404, 421, 438, 455, 473, 491, 509, 528, 547, 566
Offset: 0

Views

Author

Jonathan Vos Post, Feb 27 2007

Keywords

Comments

Kurz proved the polyomino equivalent of this conjecture as A122133 and abstracts: "In this article we prove a conjecture of Bezdek, Brass and Harborth concerning the maximum volume of the convex hull of any facet-to-facet connected system of n unit hypercubes in the d-dimensional Euclidean space. For d=2 we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each n."

Examples

			a(10) = 24 because floor((10^2 + 14*10/3 + 1)/6) = floor(24.6111111) = 24.

Links

Crossrefs

Cf. A000228, A036359, A002216, A005963, A001998, A018190, A001207, A057973, A122133.

Programs

  • Mathematica
    Table[Floor[(n^2+14n/3+1)/6],{n,0,80}] (* Harvey P. Dale, Apr 11 2012 *)
  • PARI
    concat(0, Vec(x*(1 +x^2)*(1 -x^3 +2*x^4 -x^6 +x^7 +x^11 -x^13 +x^14 +x^15 -x^16) / ((1 -x)^3*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 -x^3 +x^6)*(1 +x^3 +x^6)) + O(x^50))) \\ Colin Barker, Oct 13 2016
  • PARI
    a(n) = (n^2 + 14*n/3 + 1)\6 \\ Charles R Greathouse IV, Oct 13 2016

Formula

a(n) = floor((n^2 + 14*n/3 + 1)/6).
G.f.: x*(1 +x^2)*(1 -x^3 +2*x^4 -x^6 +x^7 +x^11 -x^13 +x^14 +x^15 -x^16) / ((1 -x)^3*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 -x^3 +x^6)*(1 +x^3 +x^6)). - Colin Barker, Oct 13 2016

Extensions

More terms from Harvey P. Dale, Apr 11 2012
Offset changed to 0 by Colin Barker, Oct 13 2016

A038145 Number of n-celled helicenes without holes.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 8, 71, 542, 3857
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • J. V. Knop et al., On the total number of polyhexes, Match, No. 16 (1984), 119-134.

Links

Crossrefs

Cf. A018190, A038143-A038147.

A039626 Number of planar simply-connected mono-q-polyhexes for q=4.

Original entry on oeis.org

1, 1, 4, 13, 57, 255, 1224, 5953
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, Studies of some chemically relevant polygonal systems: mono-q-polyhexes, ACH Models in Chem., 133(3) (1996), 277-298.

Crossrefs

Cf. A018190.

A039627 Number of planar simply-connected mono-q-polyhexes for q=3.

Original entry on oeis.org

1, 1, 3, 11, 43, 191, 884, 4195
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Brunvoll, B. N. Cyvin, and S. J. Cyvin, Studies of some chemically relevant polygonal systems: mono-q-polyhexes, ACH Models in Chem., 133(3) (1996), 277-298.

Crossrefs

Cf. A018190.

A039628 Number of planar simply-connected mono-q-polyhexes for q=2.

Original entry on oeis.org

1, 1, 3, 9, 32, 130, 566, 2548
Offset: 1

Views

Author

N. J. A. Sloane

Keywords

References

  • J. Brunvoll et al., Studies of some chemically relevant polygonal system mono-q-polyhexes, ACH Models in Chem., 133 (3) (1996), 277-298.

Crossrefs

Cf. A018190.

A120371 Number of isomers of polyhex hydrocarbons with C_(2h) symmetry with eighteen hexagons.

Original entry on oeis.org

1, 14, 59, 206, 601, 1602, 3832, 8050, 14601, 22472, 24071, 14756
Offset: 52

Views

Author

Parthasarathy Nambi, Aug 27 2006

Keywords

Comments

See Table 3 column 3 on page 614 of the paper by Caporossi and Hansen. Also the sequence starts for the hydrocarbon C_52H_18. If the number of carbons is an odd number then the number of isomers with this symmetry is zero.

Examples

			If the number of carbons is 54 then the number of isomers of polyhex hydrocarbons with C_(2h) symmetry with eighteen hexagons is 14 which is the third term in the sequence.

References

  • G. Caporossi and P. Hansen, "Enumeration of Polyhex Hydrocarbons to h=21", J. Chem. Inf. Comput. Sci., vol. 38 (1998) pp. 610-619.

Crossrefs

Cf. A018190.

A120386 Number of isomers of polyhex hydrocarbons with C_(2h) symmetry with nineteen hexagons.

Original entry on oeis.org

0, 3, 17, 66, 189, 589, 1677, 3829, 7948, 15649, 25543, 26931, 15472
Offset: 54

Views

Author

Parthasarathy Nambi, Aug 27 2006

Keywords

Comments

See Table 4 column 3 on page 615 of the paper by Caporossi and Hansen. Also the sequence starts for the hydrocarbon C_54H_18. If the number of carbons is an odd number then the number of isomers with this symmetry is zero.

Examples

			If the number of carbons is 56 then the number of isomers of polyhex hydrocarbons with C_(2h) symmetry with nineteen hexagons is 3 which is the third term in the sequence.

References

  • G. Caporossi and P. Hansen, "Enumeration of Polyhex Hydrocarbons to h=21", J. Chem. Inf. Comput. Sci., vol. 38 (1998) pp. 610-619.

Crossrefs

Cf. A018190.

A120448 Number of isomers of polyhex hydrocarbons with C_(2v) symmetry with nineteen hexagons.

Original entry on oeis.org

0, 3, 17, 14, 92, 60, 316, 175, 814, 495, 2323, 1402, 6037, 3113, 12851, 6200, 24710, 11851, 46152, 18123, 72151, 18007, 74547, 8970, 40141
Offset: 54

Views

Author

Parthasarathy Nambi, Aug 27 2006

Keywords

Comments

See Table 4 column 9 on page 615 of the paper by Caporossi and Hansen. Also the sequence starts for the hydrocarbon C_(54)H_(18).

Examples

			If the number of carbons is 56 then the number of isomers of polyhex hydrocarbons with C_(2v) symmetry with nineteen hexagons is 17 which is the third term in the sequence.

References

  • G. Caporossi and P. Hansen, "Enumeration of Polyhex Hydrocarbons to h=21", J. Chem. Inf. Comput. Sci., vol. 38 (1998) pp. 610-619.

Crossrefs

Cf. A018190.

A121950 Number of isomeric aza-benzenoids with two nitrogen atoms and n hexagons.

Original entry on oeis.org

3, 10, 48, 243, 1326, 7349, 41030, 228694, 1270663, 7031737
Offset: 1

Views

Author

Parthasarathy Nambi, Sep 04 2006

Keywords

Examples

			In a single hexagon (benzene), any 2 of the 6 carbon atoms can be chosen to be replaced by nitrogen, and it can be done in 3 ways, obtaining pyridazine, pyrimidine, or pyrazine, so a(1) = 3. For a(2) = 10, see the corresponding column of Table 7 from Trinajstić et al.

Links

Crossrefs

Cf. A018190, A121949, A121951, A121952, A121972, A121973, A121975, A121974.

Extensions

a(1) corrected by Andrey Zabolotskiy, Nov 19 2023
Previous Showing 21-30 of 30 results.

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

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