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 A035842 Coordination sequence for A_16 lattice. 0
 1, 272, 18632, 579632, 10501172, 127485584, 1135620536, 7907476016, 45076309166, 217815522736, 916470530808, 3429182092560, 11603837100660, 35995371261360, 103501142484360, 278406848295312, 705951252118284, 1698353774374704, 3897769097766104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(0) is not an element of the recurrence. - Georg Fischer, Jul 18 2020 LINKS 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 (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1). FORMULA 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. MAPLE 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 MATHEMATICA 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 *) CROSSREFS Sequence in context: A168372 A023907 A281691 * A000518 A230531 A283230 Adjacent sequences:  A035839 A035840 A035841 * A035843 A035844 A035845 KEYWORD nonn,easy AUTHOR Joan Serra-Sagrista (jserra(AT)ccd.uab.es) EXTENSIONS a(17)-a(18) from Georg Fischer, Jul 18 2020 STATUS approved

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Last modified August 3 14:46 EDT 2020. Contains 336198 sequences. (Running on oeis4.)