A213350 8-quantum transitions in systems of N >= 8 spin 1/2 particles, in columns by combination indices.

1, 18, 180, 10, 1320, 220, 7920, 2640, 66, 41184, 22880, 1716, 192192, 160160, 24024, 364, 823680, 960960, 240240, 10920, 3294720, 5125120, 1921920, 174720, 1820, 12446720, 24893440, 13069056, 1980160, 61880, 44808192, 112020480

Offset

8,2

Comments

For a general discussion, please see A213343.

This a(n) is for octuple-quantum transitions (q = 8).

It lists the flattened triangle T(8;N,k) with rows N = 8,9,... and columns k = 0..floor((N-8)/2).

References

See A213343

Links

Stanislav Sykora, Table of n, a(n) for n = 8..2216

Stanislav Sykora, T(8;N,k) with rows N = 8..100 and columns k = 0..floor((N-8)/2)

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

Formula

Set q = 8 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-8)/2)
  ---+------------------------------
   8 |    1
   9 |   18
  10 |  180   10
  11 | 1320  220
  12 | 7920 2640 66

Mathematica

With[{q = 8}, 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 = 8

Crossrefs

Cf. A051288 (q=0), A213343 to A213349 (q=1 to 7), A213351 (q=9), A213352 (q= 10).

Cf. A140325 (first row, with offset 8), A004314 (row sums).

Sequence in context: A321951 A227023 A239581 * A052507 A071910 A121038

Adjacent sequences: A213347 A213348 A213349 * A213351 A213352 A213353

Keyword

nonn,tabl

Author

Stanislav Sykora, Jun 13 2012

Status

approved