A035888 - OEIS

%I #16 Sep 05 2023 15:50:09

%S 1,0,1152,0,221952,0,17282432,0,733189632,0,19804348032,0,

%T 375290947840,201326592,5335230402432,21810380800,59807438318592,

%U 824432394240,549355033319552,17077528166400,4260137204788992

%N Coordination sequence for diamond structure D^+_24. (Edges defined by l_1 norm = 1.)

%H Ray Chandler, <a href="/A035888/b035888.txt">Table of n, a(n) for n = 0..1000</a>

%H J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).

%H Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

%H <a href="/index/Rec#order_48">Index entries for linear recurrences with constant coefficients</a>, signature (0, 24, 0, -276, 0, 2024, 0, -10626, 0, 42504, 0, -134596, 0, 346104, 0, -735471, 0, 1307504, 0, -1961256, 0, 2496144, 0, -2704156, 0, 2496144, 0, -1961256, 0, 1307504, 0, -735471, 0, 346104, 0, -134596, 0, 42504, 0, -10626, 0, 2024, 0, -276, 0, 24, 0, -1).

%p 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=24.

%K nonn

%O 0,3

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

%E Recomputed by _N. J. A. Sloane_, Nov 27 1998