OFFSET
0,2
REFERENCES
M. O'Keeffe, Coordination sequences for lattices, Zeit. f. Krist., 210 (1995), 905-908.
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
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 (6,-15,20,-15,6,-1).
FORMULA
a(n) = 6*n*(3*n^4 + 5*n^2 + 1), n > 0.
G.f.: (1+48*x+519*x^2+1024*x^3+519*x^4+48*x^5+x^6)/(1-x)^6.
E.g.f.: 1 + 6*exp(x)*x*(9 + 60*x + 80*x^2 + 30*x^3 + 3*x^4). - Stefano Spezia, Apr 15 2022
MATHEMATICA
Join[{1}, Table[18 n^5+30 n^3+6 n, {n, 30}]] (* Harvey P. Dale, May 16 2012 *)
PROG
(Magma) [1] cat [6*n*(3*n^4+5*n^2+1): n in [1..40]]; // G. C. Greubel, May 30 2023
(SageMath) [6*n*(3*n^4+5*n^2+1) +int(n==0) for n in range(41)] # G. C. Greubel, May 30 2023
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
STATUS
approved