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A008377 Crystal ball sequence for D_9 lattice.

%I A008377 #32 May 11 2024 05:15:17
%S A008377 1,145,4339,55171,416773,2218645,9195511,31608967,94016137,249258777,
%T A008377 601883259,1345167627,2817026445,5581287453,10542186111,19101404943,
%U A008377 33368594193,56438048673,92746082819,148525641875,232376811797,355974143909,534934092551,789868374935
%N A008377 Crystal ball sequence for D_9 lattice.
%H A008377 Vincenzo Librandi, <a href="/A008377/b008377.txt">Table of n, a(n) for n = 0..1000</a>
%H A008377 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 A008377 <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>
%H A008377 <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 A008377 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 A008377 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 A008377 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 A008377 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 A008377 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 A008377 nonn,easy
%O A008377 0,2
%A A008377 _N. J. A. Sloane_ and _J. H. Conway_
%E A008377 More terms from _Vincenzo Librandi_, Oct 15 2013