A008362 Crystal ball sequence for D_8 lattice.

1, 113, 2705, 28129, 177697, 807505, 2908337, 8818625, 23429185, 56070193, 123302609, 252868001, 489082465, 899992081, 1586639089, 2694819713, 4429746305, 7074058225, 11009657617, 16743877985, 24940525217, 36456362449, 52383641905, 74099318593, 103321612481

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 (9,-36,84,-126,126,-84,36,-9,1).

Programs

Magma

[248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+ 144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1: n in [0..30]]; // Vincenzo Librandi, Apr 16 2012

Maple

248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1;

Mathematica

CoefficientList[Series[(1+104*x+1724*x^2+ 7768* x^3+12550*x^4+7768*x^5+ 1724*x^6+ 104*x^7+ x^8)/(1-x)^9,{x,0,1003}],x] (* Vincenzo Librandi, Apr 16 2012 *)
LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,113,2705,28129,177697,807505,2908337,8818625,23429185},20] (* Harvey P. Dale, Sep 20 2024 *)

Formula

a(n) = 248/315*n^8+992/315*n^7+32/3*n^6+944/45*n^5+144/5*n^4+1184/45*n^3+992/63*n^2+584/105*n+1 (see MAPLE line).

G.f.: (1+104*x+1724*x^2+7768*x^3+12550*x^4+7768*x^5+1724*x^6+104*x^7+x^8)/(1-x)^9. - Colin Barker, Mar 16 2012