OFFSET
0,2
COMMENTS
Equally, coordination sequence for 6-dimensional cyclotomic lattice Z[zeta_14].
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.
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.
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 (6,-15,20,-15,6,-1).
FORMULA
G.f.: (x^6+8*x^5+29*x^4+64*x^3+29*x^2+8*x+1)/(x-1)^6. [Conway-Sloane] - Colin Barker, Sep 21 2012
a(n) = (7/6)*n*(n^2+2)*(n^2+3) for n>0, a(0)=1. - Bruno Berselli, Feb 28 2013
E.g.f.: 1 + x*(84 + 210*x + 210*x^2 + 70*x^3 + 7*x^4)*exp(x)/6. - G. C. Greubel, Nov 10 2019
MAPLE
1, seq( (7*k^5+35*k^3+42*k)/6, k=1..40);
MATHEMATICA
CoefficientList[Series[(x^6 +8x^5 +29x^4 +64x^3 +29x^2 +8x +1)/(x-1)^6, {x, 0, 50}], x] (* Vincenzo Librandi, Jun 20 2013 *)
Table[If[n==0, 1, 7*n*(6+5*n^2+n^4)/6], {n, 0, 40}] (* G. C. Greubel, Nov 10 2019 *)
PROG
(PARI) vector(46, n, if(n==1, 1, 7*(n-1)*(6+5*(n-1)^2+(n-1)^4)/6 ) ) \\ G. C. Greubel, Nov 10 2019
(Magma) [1] cat [7*n*(6+5*n^2+n^4)/6: n in [1..45]]; // G. C. Greubel, Nov 10 2019
(Sage) [1]+[7*n*(6+5*n^2+n^4)/6 for n in (1..45)]; # G. C. Greubel, Nov 10 2019
(GAP) Concatenation([1], List([1..45], n-> 7*n*(6+5*n^2+n^4)/6 )); # G. C. Greubel, Nov 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved