A001361 Number of points in interior of n-th crystal ball in E_8 lattice.

1, 241, 26641, 338401, 2240161, 10242001, 36638641, 109907521, 288653761, 683158321, 1486914001, 3020862241, 5793372001, 10579330321, 18522042481, 31261968001, 51096647041, 81176500081, 125741512081, 190404140641, 282484116001, 411401129041, 589131731761

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

G. Nebe and N. J. A. Sloane, Home page for this lattice

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

G.f.: -x*(x^8 + 232*x^7 + 7228*x^6 + 55384*x^5 + 133510*x^4 + 107224*x^3 + 24508*x^2 + 232*x + 1)/(x - 1)^9. - Colin Barker, Oct 29 2012

Maple

a:= n-> 57/7*n^8-108/7*n^7+30*n^6-72*n^5+39*n^4-36*n^3+300/7*n^2+24/7*n+1:
seq (a(n), n=1..30);

Mathematica

CoefficientList[Series[-(x^8 + 232 x^7 + 7228 x^6 + 55384 x^5 + 133510 x^4 + 107224 x^3 + 24508 x^2 + 232 x + 1)/(x - 1)^9, {x, 0, 40}], x] (* Vincenzo Librandi, Oct 13 2013 *)

Crossrefs

Cf. A008340, A008349.

Sequence in context: A094732 A119728 A133327 * A206842 A206834 A206896

Adjacent sequences: A001358 A001359 A001360 * A001362 A001363 A001364

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved