OFFSET
0,2
COMMENTS
Coordination sequence for 4-dimensional cyclotomic lattice Z[zeta_10].
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.
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 +6*x +16*x^2 +6*x^3 +x^4)/(1-x)^4. - Colin Barker, Sep 21 2012
E.g.f.: 1 + x*(10 + 15*x + 5*x^2)*exp(x). - G. C. Greubel, Nov 10 2019
MAPLE
1, seq( 5*k^3+5*k, k=1..40);
MATHEMATICA
CoefficientList[Series[(1 +6x +16x^2 +6x^3 +x^4)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Oct 15 2013 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 10, 50, 150, 340}, 40] (* Harvey P. Dale, Jun 09 2016 *)
PROG
(PARI) a(n)=5*n*(n^2+1) \\ Charles R Greathouse IV, Mar 08 2013
(Magma) [1] cat [5*n*(1+n^2): n in [1..45]]; // G. C. Greubel, Nov 10 2019
(Sage) [1]+[5*n*(1+n^2) for n in (1..45)] # G. C. Greubel, Nov 10 2019
(GAP) Concatenation([1], List([1..45], n-> 5*n*(1+n^2))); # G. C. Greubel, Nov 10 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved