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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 (list; graph; refs; listen; history; text; internal format)
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
AUTHOR
EXTENSIONS
More terms from Vincenzo Librandi, Oct 15 2013
STATUS
approved

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Last modified March 1 20:05 EST 2024. Contains 370443 sequences. (Running on oeis4.)