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A035900 Coordination sequence for diamond structure D^+_48. (Edges defined by l_1 norm = 1.) 1
1, 0, 4608, 0, 3542016, 0, 1091884544, 0, 181095585792, 0, 18801236605440, 0, 1341056098444288, 0, 70018291338395136, 0, 2802193910116429824, 0, 89036073583109693952, 0, 2309183244948006190080, 0, 49996383212627286763008, 0, 920640053898922498852864, 6755399441055744, 14645996946213859816229376 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Is this the same as A035785? - R. J. Mathar, Oct 20 2008

LINKS

Georg Fischer, Table of n, a(n) for n = 0..200

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.

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=48.

MATHEMATICA

n = 48;

f[m_] := Module[{k, 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];

f /@ Range[0, 22, 2] (* Jean-Fran├žois Alcover, Apr 07 2020, from Maple *)

CROSSREFS

Sequence in context: A032745 A020437 A157364 * A078094 A159205 A170795

Adjacent sequences:  A035897 A035898 A035899 * A035901 A035902 A035903

KEYWORD

nonn

AUTHOR

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

EXTENSIONS

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

Zeroes inserted by Georg Fischer, Jul 26 2020

STATUS

approved

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Last modified August 11 20:13 EDT 2022. Contains 356067 sequences. (Running on oeis4.)