|
|
A035885
|
|
Coordination sequence for diamond structure D^+_18. (Edges defined by l_1 norm = 1.)
|
|
1
|
|
|
1, 0, 648, 0, 70416, 0, 3116952, 0, 76117536, 131072, 1205253288, 22413312, 13740702000, 784465920, 121013567928, 13231325184, 863382367296, 141764198400, 5162116908744, 1105760747520, 26542312890192, 6802103992320, 119826539041752, 34758003916800, 483178115916384
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).
Index entries for linear recurrences with constant coefficients, signature (0, 18, 0, -153, 0, 816, 0, -3060, 0, 8568, 0, -18564, 0, 31824, 0, -43758, 0, 48620, 0, -43758, 0, 31824, 0, -18564, 0, 8568, 0, -3060, 0, 816, 0, -153, 0, 18, 0, -1).
|
|
MAPLE
|
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=18.
|
|
MATHEMATICA
|
f[m_] := Module[{n = 18, t1}, t1 = 2^(n-1)*Binomial[(n+2m)/2 - 1, n-1]; If[EvenQ[m], t1 = t1 + Sum[2^k*Binomial[n, k]* Binomial[m-1, k-1], {k, 0, n}]]; t1];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|