A213348 6-quantum transitions in systems of N >= 6 spin 1/2 particles, in columns by combination indices.

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

See A213343

Links

Stanislav Sykora, Table of n, a(n) for n = 6..2309

Stanislav Sykora, T(6;N,k) with rows N = 6..100 and columns k = 0..floor((N-6)/2)

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

Adjacent sequences: A213345 A213346 A213347 * A213349 A213350 A213351

Keyword

nonn,tabf

Author

Stanislav Sykora, Jun 13 2012

Status

approved