A008529 Coordination sequence for 4-dimensional face-centered cubic orthogonal lattice.

1, 14, 68, 202, 456, 870, 1484, 2338, 3472, 4926, 6740, 8954, 11608, 14742, 18396, 22610, 27424, 32878, 39012, 45866, 53480, 61894, 71148, 81282, 92336, 104350, 117364, 131418, 146552, 162806, 180220, 198834, 218688, 239822, 262276, 286090, 311304, 337958, 366092, 395746, 426960

Offset

0,2

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. 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+x)^2*(1+8*x+x^2)/(1-x)^4. - Colin Barker, Apr 14 2012

E.g.f.: 1 + (42 + 60*x^2 + 20*x^3)*exp(x)/3. - G. C. Greubel, Nov 09 2019

Maple

1, seq( (20*k^3+22*k)/3, k=1..45);

Mathematica

CoefficientList[Series[(1+x)^2*(1+8*x+x^2)/(1-x)^4, {x, 0, 45}], x] (* Vincenzo Librandi, Apr 16 2012 *)
Table[If[n==0, 1, 2*n*(11 +10*n^2)/3], {n, 0, 45}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 14, 68, 202, 456}, 46] (* G. C. Greubel, Nov 09 2019 *)

Prog

(Magma) [1] cat [(20*n^3+22*n)/3: n in [1..45]]; // Vincenzo Librandi, Apr 16 2012
(PARI) vector(46, n, if(n==1, 1, 2*(n-1)*(11 +10*(n-1)^2)/3) ) \\ G. C. Greubel, Nov 09 2019
(Sage) [1]+[2*n*(11 +10*n^2)/3 for n in (1..45)]; # G. C. Greubel, Nov 09 2019
(GAP) Concatenation([1], List([1..45], n-> 2*n*(11 +10*n^2)/3 )); # G. C. Greubel, Nov 09 2019

Crossrefs

Sequence in context: A064096 A250141 A071616 * A075480 A236164 A254004

Adjacent sequences: A008526 A008527 A008528 * A008530 A008531 A008532

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved