Search: id:A119800
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%I A119800
%S A119800 4,8,6,12,18,8,16,38,32,10,20,66,88,50,12,24,102,192,170,72,14,28,146,
%T A119800 360,450,292,98,16,32,198,608,1002,912,462,128,18,36,258,952,1970,2364,
%U A119800 1666,688,162,20,326,1408,3530,5336,4942,2816,978,200,1992,5890,10836
%N A119800 Array of coordination sequences for cubic lattices (rows) and of numbers 
               of L1 forms in cubic lattices (columns) (array read by antidiagonals).
%D A119800 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination 
               Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389.
%D A119800 J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information 
               Processing Letters, 76, no. 1-2 (2000), 39-44.
%H A119800 Thomas Wieder, <a href="http://www.thomas-wieder.privat.t-online.de/">
               Home Page</a>.
%H A119800 Thomas Wieder, <a href="http://homepages.tu-darmstadt.de/~wieder">(Old) 
               Home Page</a>.
%F A119800 a(m,n) = a(m,n-1)+a(m-1,n)+a(m-1,n-1), a(m,0)=1, a(0,0)=1, a(0,n)=2.
%e A119800 The second row of the table is: 6, 18, 38, 66, 102, 146, 198, 258, 326, 
               ... = A005899 = number of points on surface of octahedron.
%e A119800 The third column of the table is: 12, 38, 88, 170, 292, 462, 688, 978, 
               1340,
%e A119800 .. = A035597 = number of points of L1 norm 3 in cubic lattice Z^n.
%e A119800 The first rows are: A008574, A005899, A008412, A008413, A008414, A008415, 
               A008416, A008418, A008420.
%e A119800 The first columns are: A005843, A001105, A035597, A035598, A035599, A035600, 
               A035601, A035602, A035603.
%e A119800 The main diagonal seems to be A050146.
%o A119800 Excel cell formula: =Z(-1)S(-1)+Z(-1)S+ZS(-1). The very first row (not 
               included into the table) contains the initialization values: 1, 2, 
               2, 2, 2, 2, 2, 2, 2, 2, ... The very first column (not included into 
               the table) contains the initialization values: 1, 1, 1, 1, 1, 1, 
               1, 1, 1, 1, ... Note that the first cell is common to both the initialization 
               row and initialization column and it equal to 1.
%Y A119800 Cf. A008574, A005899, A008412, A008413, A008414, A008415, A008416, A008418, 
               A008420, A005843, A005843, A001105, A035597, A035598, A035599, A035600, 
               A035601, A035602, A035603, A050146.
%Y A119800 Sequence in context: A011515 A005531 A064494 this_sequence A063723 A028269 
               A019650
%Y A119800 Adjacent sequences: A119797 A119798 A119799 this_sequence A119801 A119802 
               A119803
%K A119800 easy,nonn,tabl
%O A119800 0,1
%A A119800 Thomas Wieder (thomas.wieder(AT)t-online.de), Jul 30 2006, Aug 06 2006

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