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A019563 Coordination sequence for C_7 lattice.

%I A019563 #34 Sep 08 2022 08:44:44
%S A019563 1,98,1666,12642,59906,209762,596610,1459810,3188738,6376034,11879042,
%T A019563 20889442,35011074,56345954,87588482,132127842,194158594,278799458,
%U A019563 392220290,541777250,736156162,985524066
%N A019563 Coordination sequence for C_7 lattice.
%H A019563 Seiichi Manyama, <a href="/A019563/b019563.txt">Table of n, a(n) for n = 0..10000</a>
%H A019563 M. Baake and U. Grimm, <a href="https://arxiv.org/abs/cond-mat/9706122">Coordination sequences for root lattices and related graphs</a>, arXiv:cond-mat/9706122, Zeit. f. Kristallographie, 212 (1997), 253-256.
%H A019563 R. Bacher, P. de la Harpe and B. Venkov, <a href="https://doi.org/10.5802/aif.1689">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
%H A019563 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A019563 G.f.: (x + 1)*(1 + 90*x + 911*x^2 + 2092*x^3 + 911*x^4 + 90*x^5 + x^6)/(1 - x)^7.
%F A019563 a(n) = A008415(2*n). - _Seiichi Manyama_, Jun 08 2018
%p A019563 seq(coeff(series((x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4+90*x^5+x^6)/(1-x)^7,x,n+1), x, n), n = 0 .. 30); # _Muniru A Asiru_, Dec 08 2018
%t A019563 Join[{1}, LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {98, 1666, 12642, 59906, 209762, 596610, 1459810}, 21]] (* _Jean-François Alcover_, Dec 08 2018 *)
%o A019563 (PARI) my(x='x+O('x^30)); Vec((x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4 + 90*x^5+x^6)/(1-x)^7) \\ _G. C. Greubel_, Dec 08 2018
%o A019563 (Magma) m:=30; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!( (x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4 + 90*x^5+x^6)/(1-x)^7 )); // _G. C. Greubel_, Dec 08 2018
%o A019563 (Sage) s=((x+1)*(1+90*x+911*x^2+2092*x^3+911*x^4 + 90*x^5+x^6)/(1-x)^7 ).series(x, 30); s.coefficients(x, sparse=False) # _G. C. Greubel_, Dec 08 2018
%Y A019563 Cf. A008415.
%K A019563 nonn
%O A019563 0,2
%A A019563 Michael Baake (mbaake(AT)sunelc3.tphys.physik.uni-tuebingen.de)