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

Author

Stanislav Sykora, Jun 13 2012

Keywords

• nonn
• tabf

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).

Examples

			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
		

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.

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).

Programs

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 *)

PARI

See A213343; set thisq = 6

Formula

Set q = 6 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).