A213346 4-quantum transitions in systems of N>=4 spin 1/2 particles, in columns by combination indices.

1, 10, 60, 6, 280, 84, 1120, 672, 28, 4032, 4032, 504, 13440, 20160, 5040, 120, 42240, 88704, 36960, 2640, 126720, 354816, 221760, 31680, 495, 366080, 1317888, 1153152, 274560, 12870, 1025024, 4612608, 5381376, 1921920, 180180, 2002

Offset: 4

Author

Stanislav Sykora, Jun 12 2012

Keywords

• tabl
• nonn

Comments

For a general discussion, please see A213343.

This a(n) is for quadruple-quantum transitions (q = 4).

It lists the flattened triangle T(4;N,k) with rows N = 4,5,... and columns k = 0..floor((N-4)/2).

Examples

			Starting rows of the triangle:
  N | k = 0, 1, ..., floor((N-4)/2)
  4 |    1
  5 |   10
  6 |   60   6
  7 |  280  84
  8 | 1120 672 28
		

References

• See A213343.

Links

• Stanislav Sykora, Table of n, a(n) for n = 4..2404
• Stanislav Sykora, T(4;N,k) with rows N=4,..,100 and columns k=0,..,floor((N-4)/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 A213345 (q=1 to 3), A213347 to A213352 (q=5 to 10).

Cf. A003472 (first column), A004310 (row sums).

Programs

Mathematica

With[{q = 4}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 14}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

PARI

See A213343; set thisq = 4

Formula

Set q = 4 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k)