A008377 Crystal ball sequence for D_9 lattice.

1, 145, 4339, 55171, 416773, 2218645, 9195511, 31608967, 94016137, 249258777, 601883259, 1345167627, 2817026445, 5581287453, 10542186111, 19101404943, 33368594193, 56438048673, 92746082819, 148525641875, 232376811797, 355974143909, 534934092551, 789868374935

Offset: 0

Author

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

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, 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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Programs

Maple

1006/2835*n^9-503/315*n^8+6404/945*n^7-244/15*n^6+3946/135*n^5-542/15*n^4+87068/2835*n^3-5356/315*n^2+1867/315*n-1;

Mathematica

CoefficientList[Series[(x + 1) (x^8 + 134 x^7 + 2800 x^6 + 15386 x^5 + 27742 x^4 + 15386 x^3 + 2800 x^2 + 134 x + 1)/(x - 1)^10, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,145,4339,55171,416773,2218645,9195511,31608967,94016137,249258777},30] (* Harvey P. Dale, May 11 2024 *)

Formula

a(n-1) = 1006/2835*n^9-503/315*n^8+6404/945*n^7-244/15*n^6+3946/135*n^5-542/15*n^4+87068/2835*n^3-5356/315*n^2+1867/315*n-1.

G.f.: (x+1) * (x^8 +134*x^7 +2800*x^6 +15386*x^5 +27742*x^4 +15386*x^3 +2800*x^2 +134*x +1) / (x-1)^10. [Colin Barker, May 28 2012]

Extensions

More terms from Vincenzo Librandi, Oct 15 2013