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A103883 Square array T(n,k) read by antidiagonals: coordination sequence for lattice B_n. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,3

LINKS

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.

FORMULA

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.

EXAMPLE

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, ...

  ...

MATHEMATICA

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-Fran├žois Alcover, Feb 13 2019 *)

CROSSREFS

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

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Feb 20 2005

STATUS

approved

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Last modified October 23 12:45 EDT 2019. Contains 328345 sequences. (Running on oeis4.)