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Search: id:A103881
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| A103881 |
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Square array T(n,k) read by antidiagonals: coordination sequence for root lattice A_n. |
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+0
27
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| 1, 1, 2, 1, 6, 2, 1, 12, 12, 2, 1, 20, 42, 18, 2, 1, 30, 110, 92, 24, 2, 1, 42, 240, 340, 162, 30, 2, 56, 462, 1010, 780, 252, 36, 2, 1, 72, 812, 2562, 2970, 1500, 362, 42, 2, 1, 90, 1332, 5768, 9492, 7002, 2570, 492, 48, 2, 1, 110, 2070, 11832, 26474, 27174, 14240
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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T(n,k) is the number of integer sequences of length n+1 with sum zero and sum of absolute values 2k. [From Ron Hardin (rhhardin(AT)att.net), Feb 23 2009]
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REFERENCES
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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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M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs
J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (Abstract, pdf, ps).
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FORMULA
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T(n, k) = Sum[i=1..n, C(n+1, i)*C(k-1, i-1)*C(n-i+k, k) ], T(n, 0)=1.
G.f. of n-th row: Sum[i=0..n, C(n, i)^2*x^i ]/(1-x)^n.
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EXAMPLE
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1,2,2,2,2,2,
1,6,12,18,24,30,
1,12,42,92,162,252,
1,20,110,340,780,1500,
1,30,240,1010,2970,7002,
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CROSSREFS
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Rows include A040000, A008458, A005901, A008383, A008385, A008387, A008389, A008391, A008393, A008395, A035837, A035838, A035839, A035840, A035841-A035876. Columns include A002376, A001621. Main diagonal is in A103882.
Sequence in context: A055878 A030304 A133200 this_sequence A101024 A124730 A114283
Adjacent sequences: A103878 A103879 A103880 this_sequence A103882 A103883 A103884
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Feb 20 2005
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