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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

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Last modified November 15 22:20 EST 2018. Contains 317252 sequences. (Running on oeis4.)