A213344 2-quantum transitions in systems of N>=2 spin 1/2 particles, in columns by combination indices.

1, 6, 24, 4, 80, 40, 240, 240, 15, 672, 1120, 210, 1792, 4480, 1680, 56, 4608, 16128, 10080, 1008, 11520, 53760, 50400, 10080, 210, 28160, 168960, 221760, 73920, 4620, 67584, 506880, 887040, 443520, 55440, 792

Offset

2,2

Comments

For a general discussion, please see A213343.

This a(n) is for double-quantum transitions (q = 2).

It lists the flattened triangle T(2;N,k) with rows N = 2,3,... and columns N, k = 0..floor((N-2)/2).

References

See A213343.

Links

Stanislav Sykora, Table of n, a(n) for n = 2..2501

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

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

Formula

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

Example

For N=4, there are 4 second-quantum transitions with combination index 1: (0001,1110),(0010,1101),(0100,1011),(1000,0111).
Starting rows of the triangle:
  N | k = 0, 1, ..., floor((N-2)/2)
  2 |   1
  3 |   6
  4 |  24   4
  5 |  80  40
  6 | 240 240 15

Mathematica

With[{q = 2}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 12}, {k, 0, Floor[(n - 2)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

Prog

(PARI) See A213343; set thisq = 2.

Crossrefs

Cf. A051288 (q=0), A213343 (q=1), A213345 to A213352 (q=3..10).

Cf. A001788 (first column), A002694 (row sums).

Sequence in context: A194770 A052697 A293256 * A337023 A193429 A213278

Adjacent sequences: A213341 A213342 A213343 * A213345 A213346 A213347

Keyword

nonn,tabf

Author

Stanislav Sykora, Jun 09 2012

Status

approved