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A035840 Coordination sequence for A_14 lattice. 2

%I

%S 1,210,11130,269570,3838590,37060506,265953170,1511679210,7125357540,

%T 28818500830,102644594262,328512273390,959882556570,2593322651430,

%U 6545498596110,15564971674518,35117045235720,75613799423610,156153427053890,310601807143530

%N Coordination sequence for A_14 lattice.

%D 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.

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

%H Vincenzo Librandi, <a href="/A035840/b035840.txt">Table of n, a(n) for n = 0..1000</a>

%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_14">Index entries for linear recurrences with constant coefficients</a>, signature (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).

%F Sum_{d=1..14} C(15, d)*C(m/2-1, d-1)*C(14-d+m/2, m/2), where norm m is always even.

%F G.f.: (x^14 + 196*x^13 + 8281*x^12 + 132496*x^11 + 1002001*x^10 + 4008004*x^9 + 9018009*x^8 + 11778624*x^7 + 9018009*x^6 + 4008004*x^5 + 1002001*x^4 + 132496*x^3 + 8281*x^2 + 196*x + 1) / (x-1)^14. [_Colin Barker_, Nov 19 2012]

%t CoefficientList[Series[(x^14 + 196 x^13 + 8281 x^12 + 132496 x^11 + 1002001 x^10 + 4008004 x^9 + 9018009 x^8 + 11778624 x^7 + 9018009 x^6 + 4008004 x^5 + 1002001 x^4 + 132496 x^3 + 8281 x^2 + 196 x + 1)/(x - 1)^14, {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 21 2013 *)

%K nonn,easy

%O 0,2

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

%E More terms from _Vincenzo Librandi_, Oct 21 2013

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Last modified August 6 17:06 EDT 2020. Contains 336255 sequences. (Running on oeis4.)