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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, 162180, 178932, 196800, 215820, 236028, 257460, 280152, 304140, 329460, 356148, 384240 (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/0508136 [math.CO], 2005-2006.

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 (4,-6,4,-1).

FORMULA

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

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

E.g.f.: 1 + x*(12 + 18*x + 6*x^2)*exp(x). - G. C. Greubel, Nov 10 2019

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

1, seq( 6*k^3+6*k, k=1..45);

MATHEMATICA

CoefficientList[Series[(1+4*x+x^2)^2/(1-x)^4, {x, 0, 45}], x] (* Vincenzo Librandi, Apr 16 2012 *)

LinearRecurrence[{4, -6, 4, -1}, {1, 12, 60, 180, 408}, 45] (* G. C. Greubel, Nov 10 2019 *)

PROG

(MAGMA) [1]cat[6*n^3+6*n: n in [1..45]]; // Vincenzo Librandi, Apr 16 2012

(PARI) vector(46, n, if(n==1, 1, 6*(n-1)*(1+(n-1)^2)) ) \\ G. C. Greubel, Nov 10 2019

(Sage) [1]+[6*n*(1+n^2) for n in (1..45)] # G. C. Greubel, Nov 10 2019

(GAP) Concatenation([1], List([1..45], n-> 6*n*(1+n^2) )); # G. C. Greubel, Nov 10 2019

CROSSREFS

Sequence in context: A300758 A332544 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 August 5 21:18 EDT 2020. Contains 336213 sequences. (Running on oeis4.)