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A008530 Coordination sequence for 4-dimensional primitive di-isohexagonal orthogonal lattice. 2
1, 12, 60, 180, 408, 780, 1332, 2100, 3120, 4428, 6060, 8052, 10440, 13260, 16548, 20340, 24672, 29580, 35100, 41268, 48120, 55692, 64020, 73140, 83088, 93900, 105612, 118260, 131880, 146508 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Coordination sequence for 4-dimensional cyclotomic lattice Z[zeta_12].

REFERENCES

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

M. Beck and S. Hosten, Cyclotomic polytopes and growth series of cyclotomic lattices, arXiv math.CO/0508136

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

FORMULA

G.f.: (1+4*x+x^2)^2/(1-x)^4. [Colin Barker, Apr 14 2012]

3*a(n) = (2n+1)^3+(2n-1)^3+(n+1)^3+(n-1)^3 for n>0. [Bruno Berselli, Jan 31 2013]

EXAMPLE

3*a(5) = 2340 = (2*5+1)^3+(2*5-1)^3+(5+1)^3+(5-1)^3. [Bruno Berselli, Jan 31 2013]

MAPLE

[ seq( 6*k^3+6*k, k=0..40) ]; # (this is for n>0)

MATHEMATICA

CoefficientList[Series[(1+4*x+x^2)^2/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 16 2012 *)

PROG

(MAGMA) [1]cat[6*n^3+6*n: n in [1..40]]; // Vincenzo Librandi, Apr 16 2012

CROSSREFS

Sequence in context: A321465 A000141 A279509 * A112415 A033486 A174642

Adjacent sequences:  A008527 A008528 A008529 * A008531 A008532 A008533

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified February 20 13:33 EST 2019. Contains 320327 sequences. (Running on oeis4.)