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A213352
10-quantum transitions in systems of N >= 10 spin 1/2 particles, in columns by combination indices.
10
1, 22, 264, 12, 2288, 312, 16016, 4368, 91, 96096, 43680, 2730, 512512, 349440, 43680, 560, 2489344, 2376192, 495040, 19040, 11202048, 14257152, 4455360, 342720, 3060, 47297536, 77395968, 33860736, 4341120, 116280, 189190144, 386979840, 225738240, 43411200
OFFSET
10,2
COMMENTS
For a general discussion, please see A213343.
This a(n) is for decuple-quantum transitions (q = 10).
It lists the flattened triangle T(10;N,k) with rows N = 10,11,... and columns k = 0..floor((N-10)/2).
REFERENCES
See A213343.
LINKS
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
FORMULA
Set q = 10 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
EXAMPLE
Starting rows of the triangle:
N | k = 0, 1, ..., floor((N-10)/2)
---+-------------------------------
10 | 1
11 | 22
12 | 264 12
13 | 2288 312
14 | 16016 4368 91
MATHEMATICA
With[{q = 10}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, q, q + 10}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 20 2019 *)
PROG
(PARI) See A213343; set thisq = 10
CROSSREFS
Cf. A051288 (q=0), A213343 to A213351 (q=1 to 9).
Cf. A172242 (first column), A004316 (row sums).
Sequence in context: A010974 A022587 A143479 * A004412 A172242 A055756
KEYWORD
nonn,tabl
AUTHOR
Stanislav Sykora, Jun 13 2012
STATUS
approved