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%I #18 Sep 08 2022 08:44:36
%S 1,56,938,7688,39746,150248,455114,1171928,2668610,5521880,10585514,
%T 19068392,32622338,53439752,84361034,128991800,191829890,278402168,
%U 395411114,550891208,754375106,1017069608,1352041418,1774412696,2301566402,2953361432,3752357546,4724050088,5897114498
%N Coordination sequence for lattice {E_7}*.
%H T. D. Noe, <a href="/A008921/b008921.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/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F G.f.: (1+x)*(1 +48*x +519*x^2 +1744*x^3 +1959*x^4 +624*x^5 +x^6)/(1-x)^7.
%F From _G. C. Greubel_, Sep 13 2019: (Start)
%F a(n) = 2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5 for n>0, with a(0)=1.
%F E.g.f.: -1 + (10 +270*x +2070*x^2 +4200*x^3 +3000*x^4 +804*x^5 +68*x^6) * exp(x)/5. (End)
%p seq(`if`(n = 0, 1, 2*(34*n^6-108*n^5+370*n^4-480*n^3+451*n^2-132*n+5)/5 ), n = 0..30); # modified by _G. C. Greubel_, Sep 13 2019
%t Table[If[n==0,1, 2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5], {n,0,30}] (* _G. C. Greubel_, Sep 13 2019 *)
%o (PARI) vector(30, n, m=n-1; if(m==0, 1, 2*(5 -132*m +451*m^2 -480*m^3 +370*m^4 -108*m^5 +34*m^6)/5) ) \\ _G. C. Greubel_, Sep 13 2019
%o (Magma) [1] cat [2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5: n in [1..30]]; // _G. C. Greubel_, Sep 13 2019
%o (Sage) [1]+[2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5 for n in (1..30)] # _G. C. Greubel_, Sep 13 2019
%o (GAP) Concatenation([1], List([1..30], n-> 2*(5 -132*n +451*n^2 -480*n^3 +370*n^4 -108*n^5 +34*n^6)/5)); # _G. C. Greubel_, Sep 13 2019
%K nonn
%O 0,2
%A _N. J. A. Sloane_
%E More terms added by _G. C. Greubel_, Sep 13 2019
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