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A103884 Square array T(n,k) read by antidiagonals: coordination sequence for lattice C_n. 5
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; text; internal format)
OFFSET

2,3

LINKS

Table of n, a(n) for n=2..53.

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 (pdf).

Joan Serra-Sagrista, Enumeration of lattice points in l_1 norm, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.

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.

EXAMPLE

Array begins:

  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, ...

  ...

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} ] ] (* Jean-Fran├žois Alcover, Jan 24 2012, after formula *)

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: A326992 A013615 A209242 * A103883 A317640 A125235

Adjacent sequences:  A103881 A103882 A103883 * A103885 A103886 A103887

KEYWORD

nonn,tabl

AUTHOR

Ralf Stephan, Feb 20 2005

STATUS

approved

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Last modified October 23 14:11 EDT 2019. Contains 328345 sequences. (Running on oeis4.)