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Coordination sequence for D_10 lattice.
2

%I #31 Feb 07 2024 09:36:10

%S 1,180,6440,94620,802640,4687108,20924280,76392940,238753440,

%T 659632980,1649142216,3796582460,8156356080,16522765220,31822575640,

%U 58659933324,104054451520,178420035060,296839277160,480696051420,759737228432,1174643272260,1780196817080

%N Coordination sequence for D_10 lattice.

%H Vincenzo Librandi, <a href="/A008378/b008378.txt">Table of n, a(n) for n = 0..1000</a>

%H R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">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 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_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F G.f.: (x^10 +170*x^9 +4685*x^8 +38200*x^7 +124850*x^6 +183356*x^5 +124850*x^4 +38200*x^3 +4685*x^2 +170*x +1) / (x -1)^10. [_Colin Barker_, Nov 19 2012]

%p 1352/945*n^9+1328/63*n^7+3416/45*n^5+13136/189*n^3+1268/105*n;

%t CoefficientList[Series[(x^10 + 170 x^9 + 4685 x^8 + 38200 x^7 + 124850 x^6 + 183356 x^5 + 124850 x^4 + 38200 x^3 + 4685 x^2 + 170 x + 1)/(x - 1)^10, {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2013 *)

%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,180,6440,94620,802640,4687108,20924280,76392940,238753440,659632980,1649142216},40] (* _Harvey P. Dale_, Jun 22 2017 *)

%Y A row of array A103903.

%Y Cf. A008379 (partial sums).

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_ and _J. H. Conway_

%E More terms from _Vincenzo Librandi_, Oct 15 2013