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.

A268283 Number of distinct directed Hamiltonian cycles of the Platonic graphs (in the order of tetrahedral, cubical, octahedral, dodecahedral, and icosahedral graph).

Original entry on oeis.org

6, 12, 32, 60, 2560
Offset: 1

Views

Author

Melvin Peralta, Jan 29 2016

Keywords

Comments

a(n)/2 is the number of distinct undirected Hamiltonian cycles of the Platonic graph corresponding to a(n).

Links

Crossrefs

Cf. A052762 (tetrahedral graph), A140986 (cubical graph), A115400 (octahedral graph), A218513 (dodecahedral graph), A218514 (icosahedral graph).

A218514 Number of n-colorings of the icosahedral graph.

Original entry on oeis.org

0, 0, 0, 0, 240, 80400, 4012560, 76848240, 825447840, 6005512800, 33014872800, 146953113120, 554770648080, 1835249610480, 5448481998960, 14778817981200, 37135461679680, 87386816771520, 194264943433920, 410876964198720, 831638579799600, 1618744884780240
Offset: 0

Views

Author

Eric M. Schmidt, Oct 31 2012

Keywords

References

  • N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See p. 69.

Links

Crossrefs

Cf. A052762, A140986, A115400, A218513, A296916, A296917..

Programs

  • Maxima
    A218514(n):=n*(n-1)*(n-2)*(n-3)*(n^8 -24*n^7 +260*n^6 -1670*n^5 +6999*n^4 -19698*n^3 +36408*n^2 -40240*n +20170)$
makelist(A218514(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */
  • Sage
    def A218514(n) : return n*(n-1)*(n-2)*(n-3)*(n^8 -24*n^7 +260*n^6 -1670*n^5 +6999*n^4 -19698*n^3 +36408*n^2 -40240*n +20170);

Formula

a(n) = n(n-1)(n-2)(n-3)(n^8 -24n^7 +260n^6 -1670n^5 +6999n^4 -19698n^3 +36408n^2 -40240n +20170).
Hence a(n) = n^12 - 30*n^11 + 415*n^10 - 3500*n^9 + 20023*n^8 - 81622*n^7 + 241605*n^6 - 517360*n^5 + 780286*n^4 - 782108*n^3 + 463310*n^2 - 121020*n (cf. A296917) - N. J. A. Sloane, Dec 23 2017
G.f.: -240*x^4*(12547*x^8 +131518*x^7 +481078*x^6 +743494*x^5 +485740*x^4 +128698*x^3 +12442*x^2 +322*x +1)/(x-1)^13. [Colin Barker, Nov 06 2012]

A296918 List of coefficients of reduced chromatic polynomial of dodecahedron, highest order terms first.

Original entry on oeis.org

1, 10, 56, 230, 759, 2112, 5104, 10912, 20880, 35972, 55768, 77152, 93538, 96396, 80572, 50808, 21302, 4412
Offset: 1

Views

Author

N. J. A. Sloane, Dec 23 2017

Keywords

Comments

The first displayed equation on page 70 of Biggs is supposed to give the chromatic polynomial of the dodecahedron. However, I could not get this to produce the polynomial in A296919, which is taken from A218513.

References

  • N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See p. 69-70.

Crossrefs

Cf. A296919, A218513.

A296919 List of coefficients of chromatic polynomial of dodecahedron, highest order terms first.

Original entry on oeis.org

1, -30, 435, -4060, 27393, -142194, 589875, -2004600, 5673571, -13518806, 27292965, -46805540, 68090965, -83530946, 85371335, -71159652, 46655060, -22594964, 7171160, -1111968, 0
Offset: 1

Views

Author

N. J. A. Sloane, Dec 23 2017

Keywords

Comments

This is based on A218513, not on the expression at the top of page 70 of the Biggs reference, which I could not get to work.

Examples

			The chromatic polynomial is x^20 - 30*x^19 + 435*x^18 - 4060*x^17 + 27393*x^16 - 142194*x^15 + 589875*x^14 - 2004600*x^13 + 5673571*x^12 - 13518806*x^11 + 27292965*x^10 - 46805540*x^9 + 68090965*x^8 - 83530946*x^7 + 85371335*x^6 - 71159652*x^5 + 46655060*x^4 - 22594964*x^3 + 7171160*x^2 - 1111968*x.

References

  • N. Biggs, Algebraic Graph Theory, 2nd ed. Cambridge University Press, 1993. See p. 69-70.

Crossrefs

Cf. A218513, A218514, A296918.
Showing 1-4 of 4 results.

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

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