A008531 Coordination sequence for {A_4}* lattice.

1, 10, 50, 150, 340, 650, 1110, 1750, 2600, 3690, 5050, 6710, 8700, 11050, 13790, 16950, 20560, 24650, 29250, 34390, 40100, 46410, 53350, 60950, 69240, 78250, 88010, 98550, 109900, 122090, 135150, 149110, 164000, 179850, 196690, 214550, 233460, 253450

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
(SageMath) [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

Cf. A222408.

Sequence in context: A102915 A153780 A196507 * A337732 A372496 A051230

Adjacent sequences: A008528 A008529 A008530 * A008532 A008533 A008534

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved