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Search: id:A119800
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| A119800 |
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Array of coordination sequences for cubic lattices (rows) and of numbers of L1 forms in cubic lattices (columns) (array read by antidiagonals). |
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5
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| 4, 8, 6, 12, 18, 8, 16, 38, 32, 10, 20, 66, 88, 50, 12, 24, 102, 192, 170, 72, 14, 28, 146, 360, 450, 292, 98, 16, 32, 198, 608, 1002, 912, 462, 128, 18, 36, 258, 952, 1970, 2364, 1666, 688, 162, 20, 326, 1408, 3530, 5336, 4942, 2816, 978, 200, 1992, 5890, 10836
(list; table; graph; listen)
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OFFSET
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0,1
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REFERENCES
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J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389.
J. Serra-Sagrista, Enumeration of lattice points in l_1 norm, Information Processing Letters, 76, no. 1-2 (2000), 39-44.
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LINKS
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Thomas Wieder, Home Page.
Thomas Wieder, (Old) Home Page.
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FORMULA
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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.
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EXAMPLE
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The second row of the table is: 6, 18, 38, 66, 102, 146, 198, 258, 326, ... = A005899 = number of points on surface of octahedron.
The third column of the table is: 12, 38, 88, 170, 292, 462, 688, 978, 1340,
.. = A035597 = number of points of L1 norm 3 in cubic lattice Z^n.
The first rows are: A008574, A005899, A008412, A008413, A008414, A008415, A008416, A008418, A008420.
The first columns are: A005843, A001105, A035597, A035598, A035599, A035600, A035601, A035602, A035603.
The main diagonal seems to be A050146.
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PROGRAM
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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.
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CROSSREFS
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Cf. A008574, A005899, A008412, A008413, A008414, A008415, A008416, A008418, A008420, A005843, A005843, A001105, A035597, A035598, A035599, A035600, A035601, A035602, A035603, A050146.
Sequence in context: A011515 A005531 A064494 this_sequence A063723 A028269 A019650
Adjacent sequences: A119797 A119798 A119799 this_sequence A119801 A119802 A119803
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Thomas Wieder (thomas.wieder(AT)t-online.de), Jul 30 2006, Aug 06 2006
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