%I #11 Aug 02 2024 15:32:43

%S 1,-46,769,-5632,18688,-44032,85760,-147968,234752,-350208,498432,

%T -683520,909568,-1180672,1500928,-1874432,2305280,-2797568,3355392,

%U -3982848,4684032,-5463040,6323968,-7270912,8307968,-9439232,10668800,-12000768,13439232,-14988288

%N From expansion of Belyi function for octahedron.

%H Colin Barker, <a href="/A066405/b066405.txt">Table of n, a(n) for n = 0..1000</a>

%H N. Magot and A. Zvonkin, <a href="http://dx.doi.org/10.1016/S0012-365X(99)00266-6">Belyi functions for Archimedian solids</a>, Discrete Math., 217 (2000), 249-271.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-4,-6,-4,-1).

%F The Belyi function is 1/Belyi function for cube.

%F From _Colin Barker_, Jan 12 2016: (Start)

%F a(n) = 256*(-1)^n*(8*n^3-24*n^2+25*n-9)/3 for n>2.

%F a(n) = -4*a(n-1)-6*a(n-2)-4*a(n-3)-a(n-4) for n>6.

%F G.f.: (1-14*x+x^2)^3 / (1+x)^4.

%F (End)

%t LinearRecurrence[{-4,-6,-4,-1},{1,-46,769,-5632,18688,-44032,85760},30] (* _Harvey P. Dale_, Aug 02 2024 *)

%o (PARI) Vec((1-14*x+x^2)^3/(1+x)^4 + O(x^30)) \\ _Colin Barker_, Jan 12 2016

%Y Cf. A066402, A066403, A066404.

%K sign,easy

%O 0,2

%A _N. J. A. Sloane_, Dec 25 2001

%E Corrected by Francisco Salinas (franciscodesalinas(AT)hotmail.com), Dec 25 2001