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A103884
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Square array T(n,k) read by antidiagonals: coordination sequence for lattice C_n.
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3
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1, 1, 8, 1, 18, 16, 1, 32, 66, 24, 1, 50, 192, 146, 32, 1, 72, 450, 608, 258, 40, 1, 98, 912, 1970, 1408, 402, 48, 1, 128, 1666, 5336, 5890, 2720, 578, 56, 1, 162, 2816, 12642, 20256, 14002, 4672, 786, 64, 1, 200, 4482, 27008, 59906, 58728, 28610
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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REFERENCES
| 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
| 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
| T(n, k) = Sum[i=1..2k, 2^i*C(n, i)*C(2k-1, i-1) ], T(n, 0)=1.
G.f. of n-th row: Sum[i=0..n, C(2n, 2i)*x^i ]/(1-x)^n.
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EXAMPLE
| 1,8,16,24,32,40,48,
1,18,66,146,258,402,578,
1,32,192,608,1408,2720,4672,
1,50,450,1970,5890,14002,28610,
1,72,912,5336,20256,58728,142000,
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MATHEMATICA
| nmin = 2; nmax = 11; t[n_, 0] = 1; t[n_, k_] := 2n*Hypergeometric2F1[1-2k, 1-n, 2, 2]; tnk = Table[ t[n, k], {n, nmin, nmax}, {k, 0, nmax-nmin}]; Flatten[ Table[ tnk[[ n-k+1, k ]], {n, 1, nmax-nmin+1}, {k, 1, n} ] ] (* From Jean-François Alcover, Jan 24 2012, after formula *)
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CROSSREFS
| Rows include A022144, A010006, A019560, A019561, A019562, A019563, A019564, A035746, A035747, A035748, A035749, A035750-A035787. Columns include A001105, A035598, A035600, A035602, A035604, A035606. Main diagonal is in A103885.
Sequence in context: A040071 A126000 A013615 * A103883 A125235 A183892
Adjacent sequences: A103881 A103882 A103883 * A103885 A103886 A103887
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KEYWORD
| nonn,tabl
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AUTHOR
| Ralf Stephan, Feb 20 2005
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