A008378 Coordination sequence for D_10 lattice.
1, 180, 6440, 94620, 802640, 4687108, 20924280, 76392940, 238753440, 659632980, 1649142216, 3796582460, 8156356080, 16522765220, 31822575640, 58659933324, 104054451520, 178420035060, 296839277160, 480696051420, 759737228432, 1174643272260, 1780196817080
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- R. Bacher, P. de la Harpe and B. Venkov, Séries de croissance et séries d'Ehrhart associées aux réseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
- J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Maple
1352/945*n^9+1328/63*n^7+3416/45*n^5+13136/189*n^3+1268/105*n;
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Mathematica
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 *) 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 *)
Formula
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]
Extensions
More terms from Vincenzo Librandi, Oct 15 2013