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A035838 Coordination sequence for A_12 lattice. 2
1, 156, 6162, 112268, 1219374, 9129276, 51697802, 235895244, 907129236, 3037849828, 9079799742, 24680519604, 61908797418, 144977296932, 319917948246, 670283877588, 1341750437352, 2579499722124, 4783532975546, 8588601364668, 14977318285254, 25437258929836 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

R. Bacher, P. de la Harpe and B. Venkov, Series de croissance et series d'Ehrhart associees aux reseaux de racines, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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 (12, -66, 220, -495, 792, -924, 792, -495, 220, -66, 12, -1).

FORMULA

Sum_{d=1..12} C(13, d)*C(m/2 - 1, d - 1)*C(12 - d + m/2, m/2), where norm m is always even.

G.f.: (x^12 + 144*x^11 + 4356*x^10 + 48400*x^9 + 245025*x^8 + 627264*x^7 + 853776*x^6 + 627264*x^5 + 245025*x^4 + 48400*x^3 + 4356*x^2 + 144*x + 1) / (x - 1)^12. [Colin Barker, Nov 19 2012]

MATHEMATICA

CoefficientList[Series[(x^12 + 144 x^11 + 4356 x^10 + 48400 x^9 + 245025 x^8 + 627264 x^7 + 853776 x^6 + 627264 x^5 + 245025 x^4 + 48400 x^3 + 4356 x^2 + 144 x + 1)/(x - 1)^12, {x, 0, 30}], x] (* Vincenzo Librandi, Oct 21 2013 *)

CROSSREFS

Sequence in context: A275766 A023903 A240005 * A035824 A252778 A006112

Adjacent sequences:  A035835 A035836 A035837 * A035839 A035840 A035841

KEYWORD

nonn,easy

AUTHOR

Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

EXTENSIONS

More terms from Vincenzo Librandi, Oct 21 2013

STATUS

approved

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Last modified January 24 12:11 EST 2022. Contains 350536 sequences. (Running on oeis4.)