A115400 - OEIS

%I #28 Jan 19 2024 12:03:17

%S 0,0,0,6,96,780,4080,15330,45696,115416,257760,523710,987360,1752036,

%T 2957136,4785690,7472640,11313840,16675776,24006006,33844320,46834620,

%U 63737520,85443666,112987776,147563400,190538400,243471150,308127456

%N Number of n-colorings of the octahedral graph.

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

%H Vincenzo Librandi, <a href="/A115400/b115400.txt">Table of n, a(n) for n = 0..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OctahedralGraph.html">Octahedral Graph</a>.

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

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

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

%F 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

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

%o (Magma) [n*(n-1)*(n-2)*(n^3 - 9*n^2 + 29*n - 32): n in [0..50]]; // _Vincenzo Librandi_, Feb 12 2012

%o (Maxima) A115400(n):=n*(n-1)*(n-2)*(n^3 - 9*n^2 + 29*n - 32)$

%o makelist(A115400(n),n,0,30); /* _Martin Ettl_, Nov 03 2012 */

%Y Cf. A140986.

%K easy,nonn

%O 0,4

%A _Jonathan Vos Post_, Aug 25 2008