A035840 - OEIS

%I #27 Sep 06 2023 01:44:40

%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.

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

%H R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.

%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 Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

%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