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A008378 revision #30

A008378
Coordination sequence for D_10 lattice.
2
1, 180, 6440, 94620, 802640, 4687108, 20924280, 76392940, 238753440, 659632980, 1649142216, 3796582460, 8156356080, 16522765220, 31822575640, 58659933324, 104054451520, 178420035060, 296839277160, 480696051420, 759737228432, 1174643272260, 1780196817080
OFFSET
0,2
LINKS
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).
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]
MAPLE
1352/945*n^9+1328/63*n^7+3416/45*n^5+13136/189*n^3+1268/105*n;
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 *)
CROSSREFS
A row of array A103903.
Cf. A008379 (partial sums).
Sequence in context: A250146 A243465 A271673 * A214818 A287022 A217791
KEYWORD
nonn,easy
EXTENSIONS
More terms from Vincenzo Librandi, Oct 15 2013
STATUS
proposed