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A035842 Coordination sequence for A_16 lattice. 0

%I #22 Jul 18 2020 10:23:21

%S 1,272,18632,579632,10501172,127485584,1135620536,7907476016,

%T 45076309166,217815522736,916470530808,3429182092560,11603837100660,

%U 35995371261360,103501142484360,278406848295312,705951252118284,1698353774374704,3897769097766104

%N Coordination sequence for A_16 lattice.

%C a(0) is not an element of the recurrence. - _Georg Fischer_, Jul 18 2020

%H R. Bacher, P. de la Harpe and B. Venkov, <a href="https://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="https://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_16">Index entries for linear recurrences with constant coefficients</a>, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

%F Sum_{d=1..16} C(17, d)*C(m/2-1, d-1)*C(16-d+m/2, m/2), where norm m is always even.

%p A := (m, n) -> `if`(m=0,1,(n+1)*binomial(m+n-1,m)*hypergeom([1-m,1-n,-n],[2,-m-n+1],1)): seq(simplify(A(m, 16)), m=0..18); # _Peter Luschny_, Jul 18 2020

%t n:=16; Table[Sum[Binomial[n+1,k]*Binomial[m-1,k-1]*Binomial[n-k+m,m], {k,0,n}],{m,0,n+2}] (* _Georg Fischer_, Jul 18 2020 *)

%K nonn,easy

%O 0,2

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

%E a(17)-a(18) from _Georg Fischer_, Jul 18 2020

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)