A035882 Coordination sequence for diamond structure D^+_12. (Edges defined by l_1 norm = 1.)

1, 0, 288, 0, 14016, 0, 286048, 24576, 3441024, 745472, 28329888, 8945664, 173667392, 65175552, 843477984, 343982080, 3403653888, 1444724736, 11829909024, 5112102912, 36395000256, 15823175680, 101202780768, 43979120640, 258496529536, 111876710400

Offset

0,3

Links

Vincenzo Librandi, 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, 12, 0, -66, 0, 220, 0, -495, 0, 792, 0, -924, 0, 792, 0, -495, 0, 220, 0, -66, 0, 12, 0, -1).

Formula

G.f.: (x^24 +276*x^22 +10626*x^20 +136644*x^18 +24576*x^17 +870639*x^16 +450560*x^15 +2975016*x^14 +1622016*x^13 +4596508*x^12 +1622016*x^11 +2975016*x^10+ 450560*x^9 +870639*x^8 +24576*x^7 +136644*x^6 +10626*x^4 +276*x^2 +1) / ((x -1)^12*(x +1)^12). [Colin Barker, Feb 26 2013]

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=12.

Mathematica

CoefficientList[Series[(x^24 + 276 x^22 + 10626 x^20 + 136644 x^18 + 24576 x^17 + 870639 x^16 + 450560 x^15 + 2975016 x^14 + 1622016 x^13 + 4596508 x^12 + 1622016 x^11 + 2975016 x^10 + 450560 x^9 + 870639 x^8 + 24576 x^7 + 136644 x^6 + 10626 x^4 + 276 x^2 + 1)/((x - 1)^12 (x + 1)^12), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 21 2013 *)

Crossrefs

Sequence in context: A289339 A011817 A334008 * A244512 A214301 A296902

Adjacent sequences: A035879 A035880 A035881 * A035883 A035884 A035885

Keyword

nonn,easy

Author

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

Extensions

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

More terms from Colin Barker, Feb 26 2013

Status

approved