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

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Programs

GAP

Concatenation([1], List([1..45], n-> 2*n*(11 +10*n^2)/3 )); # G. C. Greubel, Nov 09 2019

Magma

[1] cat [(20*n^3+22*n)/3: n in [1..45]]; // Vincenzo Librandi, Apr 16 2012

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 *)

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

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