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A008362 Crystal ball sequence for D_8 lattice.

%I A008362 #34 Aug 20 2025 00:29:08
%S A008362 1,113,2705,28129,177697,807505,2908337,8818625,23429185,56070193,
%T A008362 123302609,252868001,489082465,899992081,1586639089,2694819713,
%U A008362 4429746305,7074058225,11009657617,16743877985,24940525217,36456362449,52383641905,74099318593,103321612481
%N A008362 Crystal ball sequence for D_8 lattice.
%H A008362 Vincenzo Librandi, <a href="/A008362/b008362.txt">Table of n, a(n) for n = 0..1000</a>
%H A008362 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 A008362 <a href="/index/Cor#crystal_ball">Index entries for crystal ball sequences</a>
%H A008362 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F A008362 a(n) = 248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1 (see MAPLE line).
%F A008362 G.f.: (1+104*x+1724*x^2+7768*x^3+12550*x^4+7768*x^5+1724*x^6+104*x^7+x^8)/(1-x)^9. - _Colin Barker_, Mar 16 2012
%p A008362 248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1;
%t A008362 CoefficientList[Series[(1+104*x+1724*x^2+ 7768* x^3+12550*x^4+7768*x^5+ 1724*x^6+ 104*x^7+ x^8)/(1-x)^9,{x,0,1003}],x] (* _Vincenzo Librandi_, Apr 16 2012 *)
%t A008362 LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,113,2705,28129,177697,807505,2908337,8818625,23429185},20] (* _Harvey P. Dale_, Sep 20 2024 *)
%o A008362 (Magma) [248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+ 144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1: n in [0..30]]; // _Vincenzo Librandi_, Apr 16 2012
%K A008362 nonn,easy
%O A008362 0,2
%A A008362 _N. J. A. Sloane_ and _J. H. Conway_