Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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