%I #32 May 11 2024 05:15:17

%S 1,145,4339,55171,416773,2218645,9195511,31608967,94016137,249258777,

%T 601883259,1345167627,2817026445,5581287453,10542186111,19101404943,

%U 33368594193,56438048673,92746082819,148525641875,232376811797,355974143909,534934092551,789868374935

%N Crystal ball sequence for D_9 lattice.

%H Vincenzo Librandi, <a href="/A008377/b008377.txt">Table of n, a(n) for n = 0..1000</a>

%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F a(n-1) = 1006/2835*n^9-503/315*n^8+6404/945*n^7-244/15*n^6+3946/135*n^5-542/15*n^4+87068/2835*n^3-5356/315*n^2+1867/315*n-1.

%F G.f.: (x+1) * (x^8 +134*x^7 +2800*x^6 +15386*x^5 +27742*x^4 +15386*x^3 +2800*x^2 +134*x +1) / (x-1)^10. [_Colin Barker_, May 28 2012]

%p 1006/2835*n^9-503/315*n^8+6404/945*n^7-244/15*n^6+3946/135*n^5-542/15*n^4+87068/2835*n^3-5356/315*n^2+1867/315*n-1;

%t CoefficientList[Series[(x + 1) (x^8 + 134 x^7 + 2800 x^6 + 15386 x^5 + 27742 x^4 + 15386 x^3 + 2800 x^2 + 134 x + 1)/(x - 1)^10, {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)

%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,145,4339,55171,416773,2218645,9195511,31608967,94016137,249258777},30] (* _Harvey P. Dale_, May 11 2024 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_ and _J. H. Conway_

%E More terms from _Vincenzo Librandi_, Oct 15 2013