A008390 Crystal ball sequence for A_7 lattice.

1, 57, 869, 6637, 33111, 124223, 380731, 1004307, 2360501, 5064013, 10089705, 18912785, 33681595, 57426435, 94307855, 149907847, 231567369, 348773633, 513600589, 741206037, 1050388799, 1464209383

Offset: 0

Author

N. J. A. Sloane and J. H. Conway

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 0..1000
• J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
• Index entries for crystal ball sequences
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Programs

Mathematica

LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,57,869,6637,33111,124223,380731,1004307},30] (* Harvey P. Dale, Dec 16 2017 *)

Formula

a(n) = 143/210*n^7+143/60*n^6+451/60*n^5+77/6*n^4+937/60*n^3+707/60*n^2+363/70*n+1. - T. D. Noe, Apr 29 2007

G.f.: (1+x)*(1+48*x+393*x^2+832*x^3+393*x^4+48*x^5+x^6)/(1-x)^8. - Colin Barker, Mar 16 2012