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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved