A213347 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.

1, 12, 84, 7, 448, 112, 2016, 1008, 36, 8064, 6720, 720, 29568, 36960, 7920, 165, 101376, 177408, 63360, 3960, 329472, 768768, 411840, 51480, 715, 1025024, 3075072, 2306304, 480480, 20020, 3075072, 11531520, 11531520

Offset

5,2

Comments

For a general discussion, please see A213343.

This a(n) is for quintuple-quantum transitions (q = 5).

It lists the flattened triangle T(5;N,k) with rows N = 5,6,... and columns N, k = 0..floor((N-5)/2).

References

See A213343

Links

Stanislav Sykora, Table of n, a(n) for n = 5..2356

Stanislav Sykora, T(5;N,k) with rows N=5,..,100 and columns k=0,..,floor((N-5)/2)

Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

Formula

Set q = 5 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-5)/2)
  5 |    1
  6 |   12
  7 |   84    7
  8 |  448  112
  9 | 2016 1008 36

Mathematica

With[{q = 5}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 15}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

Prog

(PARI) See A213343; set thisq = 5

Crossrefs

Cf. A051288 (q=0), A213343 to A213346 (q=1 to 4), A213348 to A213352 (q=6 to 10).

A054849 (first column), A004311 (row sums).

Sequence in context: A275743 A026949 A165127 * A075476 A298977 A213784

Adjacent sequences: A213344 A213345 A213346 * A213348 A213349 A213350

Keyword

tabf,nonn

Author

Stanislav Sykora, Jun 13 2012

Status

approved