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A008402 Crystal ball sequence for {E_6}* lattice. 1
1, 55, 883, 6085, 26461, 86491, 232975, 545833, 1151065, 2235871, 4065931, 7004845, 11535733, 18284995, 28048231, 41818321, 60815665, 86520583, 120707875, 165483541, 223323661, 297115435 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

Index entries for crystal ball sequences

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

M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908. [Annotated scanned copy]

Index entries for linear recurrences with constant coefficients, signature (7, -21, 35, -35, 21, -7, 1).

FORMULA

G.f.: (1+48*x+519*x^2+1024*x^3+519*x^4+48*x^5+x^6)/(1-x)^7.

a(0)=1, a(1)=55, a(2)=883, a(3)=6085, a(4)=26461, a(5)=86491, a(6)=232975, a(n)=7*a(n-1)-21*a(n-2)+35*a(n-3)-35*a(n-4)+ 21*a(n-5)- 7*a(n-6)+a(n-7). - Harvey P. Dale, Jun 20 2013

a(n) = 3n^6 + 9n^5 + 15n^4 + 15n^3 + 9n^2 + 3n + 1 = 1+3*n*(n+1)*(n^2+n+1)^2. - Charles R Greathouse IV, Jun 20 2013

MATHEMATICA

CoefficientList[Series[(1+48x+519x^2+1024x^3+519x^4+48x^5+x^6)/(1-x)^7, {x, 0, 30}], x] (* or *) LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {1, 55, 883, 6085, 26461, 86491, 232975}, 30] (* Harvey P. Dale, Jun 20 2013 *)

PROG

(PARI) 3*n^6+9*n^5+15*n^4+15*n^3+9*n^2+3*n+1 \\ Charles R Greathouse IV, Jun 20 2013

CROSSREFS

Sequence in context: A297523 A221786 A241634 * A281073 A203872 A297753

Adjacent sequences:  A008399 A008400 A008401 * A008403 A008404 A008405

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 15 21:12 EST 2019. Contains 320138 sequences. (Running on oeis4.)