A035885 Coordination sequence for diamond structure D^+_18. (Edges defined by l_1 norm = 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

Offset

0,3

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.

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];
Table[f[m], {m, 0, 24}] (* Jean-François Alcover, Mar 23 2023, after Maple code *)

Crossrefs

Sequence in context: A046020 A108821 A345702 * A114827 A334896 A271639

Adjacent sequences: A035882 A035883 A035884 * A035886 A035887 A035888

Keyword

nonn

Author

Joan Serra-Sagrista (jserra(AT)ccd.uab.es)

Extensions

Recomputed by N. J. A. Sloane, Nov 27 1998

Status

approved