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A213348
6-quantum transitions in systems of N >= 6 spin 1/2 particles, in columns by combination indices.
3
1, 14, 112, 8, 672, 144, 3360, 1440, 45, 14784, 10560, 990, 59136, 63360, 11880, 220, 219648, 329472, 102960, 5720, 768768, 1537536, 720720, 80080, 1001, 2562560, 6589440, 4324320, 800800, 30030, 8200192, 26357760, 23063040
OFFSET
6,2
COMMENTS
For a general discussion, please see A213343.
This a(n) is for sextuple-quantum transitions (q = 6).
It lists the flattened triangle T(6;N,k) with rows N = 6,7,... and columns k = 0..floor((N-6)/2).
REFERENCES
LINKS
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
FORMULA
Set q = 6 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-6)/2)
6 | 1
7 | 14
8 | 112 8
9 | 672 144
10 | 3360 1440 45
MATHEMATICA
With[{q = 6}, 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 = 6
CROSSREFS
Cf. A051288 (q=0), A213343 to A213347 (q=1 to 5), A213349 to A213352 (q=7 to 10).
Cf. A002409 (first column, with offset 6), A004312 (row sums).
Sequence in context: A244693 A039630 A234800 * A341368 A004408 A002409
KEYWORD
nonn,tabf
AUTHOR
Stanislav Sykora, Jun 13 2012
STATUS
approved