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 A008395 Coordination sequence for A_10 lattice. 3
 1, 110, 3080, 40370, 322190, 1815506, 7925720, 28512110, 88206140, 241925530, 601585512, 1379301990, 2953859370, 5968878630, 11472968760, 21114177018, 37403270520, 64062783510, 106481351240, 172295622730, 272125000774, 420487598410 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS T. D. Noe, Table of n, a(n) for n = 0..1000 M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122, 1997; Zeit. f. Kristallographie, 212 (1997), 253-256. 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). Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44. Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1). FORMULA a(n) = 46189/90720*n^9 +26741/3024*n^7 +171457/4320*n^5 +111683/2268*n^3 +7381/630*n for n >= 1. Sum_{d=1}^10 C(11, d) C(m/2-1, d-1) C(10-d+m/2, m/2), where norm m is always even. (Serra-Sagrista) G.f.: (1 +100*x +2025*x^2 +14400*x^3 +44100*x^4 +63504*x^5 +44100*x^6 +14400*x^7 +2025*x^8 +100*x^9 +x^10)/(1-x)^10. - Colin Barker, Sep 26 2012 MAPLE a:= n-> `if`(n=0, 1, 46189/90720*n^9+26741/3024*n^7+ 171457/4320*n^5+111683/2268*n^3+7381/630*n): seq(a(n), n=0..25); MATHEMATICA a[n_]:= If[n==0, 1, 11n(4199n^8 +72930n^6 +327327n^4 +406120n^2 +96624)/90720]; Table[a[n], {n, 0, 21}] (* Jean-François Alcover, Jan 07 2019 *) LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {1, 110, 3080, 40370, 322190, 1815506, 7925720, 28512110, 88206140, 241925530, 601585512}, 30] (* Harvey P. Dale, Nov 27 2019 *) PROG (Magma) [1] cat [11*n*(4199*n^8 +72930*n^6 +327327*n^4 +406120*n^2 +96624)/90720: n in [1..40]]; // G. C. Greubel, May 27 2023 (SageMath) [11*n*(4199*n^8 +72930*n^6 +327327*n^4 +406120*n^2 +96624)//90720 +int(n==0) for n in range(41)] # G. C. Greubel, May 27 2023 CROSSREFS Row 10 of A103881. Sequence in context: A185536 A201833 A035836 * A201213 A250528 A251029 Adjacent sequences: A008392 A008393 A008394 * A008396 A008397 A008398 KEYWORD nonn,easy AUTHOR N. J. A. Sloane and J. H. Conway STATUS approved

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Last modified September 27 08:53 EDT 2023. Contains 365674 sequences. (Running on oeis4.)