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A103883
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Square array T(n,k) read by antidiagonals: coordination sequence for lattice B_n.
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0
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1, 1, 8, 1, 18, 16, 1, 32, 74, 24, 1, 50, 224, 170, 32, 1, 72, 530, 768, 306, 40, 1, 98, 1072, 2562, 1856, 482, 48, 1, 128, 1946, 6968, 8130, 3680, 698, 56, 1, 162, 3264, 16394, 28320, 20082, 6432, 954, 64, 1, 200, 5154, 34624, 83442, 85992, 42130, 10304, 1250, 72
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OFFSET
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2,3
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LINKS
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Table of n, a(n) for n=2..56.
M. Baake and U. Grimm, Coordination sequences for root lattices and related graphs, arXiv:cond-mat/9706122 [cond-mat.stat-mech], 1997.
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.
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FORMULA
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G.f. of n-th row: (Sum_{i=0..n} (C(2n+1, 2*i) - 2*i*C(n, i))*x^i)/(1-x)^n.
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EXAMPLE
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Array begins:
1, 8, 16, 24, 32, 40, 48, ...
1, 18, 74, 170, 306, 482, 698, ...
1, 32, 224, 768, 1856, 3680, 6432, ...
1, 50, 530, 2562, 8130, 20082, 42130, ...
1, 72, 1072, 6968, 28320, 85992, 214864, ...
...
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MATHEMATICA
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offset = 2;
T[n_, k_] := SeriesCoefficient[Sum[(Binomial[2n + 1, 2i] - 2i Binomial[n, i]) x^i, {i, 0, n}]/(1 - x)^n, {x, 0, k}];
Table[T[n - k, k], {n, offset, 11}, {k, 0, n - offset}] // Flatten (* Jean-François Alcover, Feb 13 2019 *)
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CROSSREFS
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Rows include A022144, A022145, A022146, A022147, A022148, A022149, A022150, A022151, A022152, A022153, A022154. Columns include A001105. Cf. A103881.
Sequence in context: A013615 A209242 A103884 * A317640 A125235 A183892
Adjacent sequences: A103880 A103881 A103882 * A103884 A103885 A103886
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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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STATUS
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approved
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