OFFSET
0,3
COMMENTS
Also, coordination sequence for diamond structure D^+_8. (Edges defined by l_1 norm = 1.) - J. Serra-Sagrista (jserra(AT)ccd.uab.es). Confirmed by N. J. A. Sloane Nov 27 1998.
LINKS
Ray Chandler, 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).
Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
P. Solé, Counting lattice points in pyramids, Discr. Math. 139 (1995), 381-392.
Index entries for linear recurrences with constant coefficients, signature (0, 8, 0, -28, 0, 56, 0, -70, 0, 56, 0, -28, 0, 8, 0, -1).
FORMULA
G.f.: (1/2)*((1+z^2)^8+256*z^8)/(1-z^2)^8 + (1/2)*(1-z^2)^8/(1+z^2)^8.
MAPLE
1/2*((1+z^2)^8+256*z^8)/(1-z^2)^8+1/2*(1-z^2)^8/(1+z^2)^8
f := proc(m) local k, t1; t1 := 2^(n-1)*binomial((n+2*m)/2-1, n-1); if m mod 2 = 0 then t1 := t1+add(2^k*binomial(n, k)*binomial(m-1, k-1), k=0..n); fi; t1; end; where n=8.
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved