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

Offset

0,2

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).

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]

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 *)

Prog

(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

Crossrefs

Sequence in context: A079098 A187519 A301529 * A262074 A200854 A012031

Adjacent sequences: A008359 A008360 A008361 * A008363 A008364 A008365

Keyword

nonn,easy,changed

Author

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

Status

approved