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A008529
Coordination sequence for 4-dimensional face-centered cubic orthogonal lattice.
1
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
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]
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
KEYWORD
nonn,easy
STATUS
approved