A035876 Coordination sequence for A_50 lattice.

1, 2550, 1626900, 462400850, 74214929700, 7664751475110, 553532399900300, 29615721096973650, 1225039098412340850, 40483994261907371450, 1097141899359944015580, 24907942311608525171550, 482175421833854221370900

Offset: 0

Author

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

Keywords

• nonn
• easy

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 (50, -1225, 19600, -230300, 2118760, -15890700, 99884400, -536878650, 2505433700, -10272278170, 37353738800, -121399651100, 354860518600, -937845656300, 2250829575120, -4923689695575, 9847379391150, -18053528883775, 30405943383200, -47129212243960, 67327446062800, -88749815264600, 108043253365600, -121548660036300, 126410606437752, -121548660036300, 108043253365600, -88749815264600, 67327446062800, -47129212243960, 30405943383200, -18053528883775, 9847379391150, -4923689695575, 2250829575120, -937845656300, 354860518600, -121399651100, 37353738800, -10272278170, 2505433700, -536878650, 99884400, -15890700, 2118760, -230300, 19600, -1225, 50, -1).

Formula

Sum_{d=1..50} C(51, d)*C(m/2-1, d-1)*C(50-d+m/2, m/2), where norm m is always even.

Extensions

a(9)-a(10) corrected, a(11)-a(12) added by Ray Chandler, Jan 19 2016