A115400 Number of n-colorings of the octahedral graph.

0, 0, 0, 6, 96, 780, 4080, 15330, 45696, 115416, 257760, 523710, 987360, 1752036, 2957136, 4785690, 7472640, 11313840, 16675776, 24006006, 33844320, 46834620, 63737520, 85443666, 112987776, 147563400, 190538400, 243471150, 308127456

Offset

0,4

Comments

The octahedral graph is the dual of the cubical graph whose chromatic polynomial is evaluated in A140986.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Eric Weisstein's World of Mathematics, Octahedral Graph.

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = n*(n-1)*(n-2)*(n^3 - 9*n^2 + 29*n - 32).

G.f.: 6*x^3*(1 + 9*x + 39*x^2 + 71*x^3)/(1-x)^7. - Colin Barker, Feb 12 2012

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6. - Chai Wah Wu, Jan 19 2024

Mathematica

Table[n*(n-1)*(n-2)*(n^3-9*n^2+29*n-32), {n, 0, 50}] (* Vincenzo Librandi, Feb 12 2012 *)

Prog

(Magma) [n*(n-1)*(n-2)*(n^3 - 9*n^2 + 29*n - 32): n in [0..50]]; // Vincenzo Librandi, Feb 12 2012
(Maxima) A115400(n):=n*(n-1)*(n-2)*(n^3 - 9*n^2 + 29*n - 32)$
makelist(A115400(n), n, 0, 30); /* Martin Ettl, Nov 03 2012 */

Crossrefs

Cf. A140986.

Sequence in context: A303212 A226549 A053338 * A279868 A055358 A030989

Adjacent sequences: A115397 A115398 A115399 * A115401 A115402 A115403

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 25 2008

Status

approved