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

Author

Jonathan Vos Post, Aug 25 2008

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A140986.

Programs

Magma

[n*(n-1)*(n-2)*(n^3 - 9*n^2 + 29*n - 32): n in [0..50]]; // Vincenzo Librandi, Feb 12 2012

Mathematica

Table[n*(n-1)*(n-2)*(n^3-9*n^2+29*n-32),{n,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 */

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