|
| |
|
|
A001361
|
|
Number of points in interior of n-th crystal ball in E_8 lattice.
|
|
1
|
|
|
|
1, 241, 26641, 338401, 2240161, 10242001, 36638641, 109907521, 288653761, 683158321, 1486914001, 3020862241, 5793372001, 10579330321, 18522042481, 31261968001, 51096647041, 81176500081, 125741512081, 190404140641, 282484116001, 411401129041, 589131731761
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
