A213351 9-quantum transitions in systems of N >= 9 spin 1/2 particles, in columns by combination indices.

1, 20, 220, 11, 1760, 264, 11440, 3432, 78, 64064, 32032, 2184, 320320, 240240, 32760, 455, 1464320, 1537536, 349440, 14560, 6223360, 8712704, 2970240, 247520, 2380, 24893440, 44808192, 21385728, 2970240, 85680, 94595072, 212838912, 135442944, 28217280

Offset

9,2

Comments

For a general discussion, please see A213343.

This a(n) is for nonuple-quantum transitions (q = 9).

It lists the flattened triangle T(9;N,k) with rows N = 9,10,... and columns k = floor((N-9)/2).

References

See A213343

Links

Stanislav Sykora, Table of n, a(n) for n = 9..2170

Stanislav Sykora, T(9;N,k) with rows N = 9..100 and columns k = 0..floor((N-9)/2)

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

Formula

Set q = 9 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-9)/2)
  ---+------------------------------
   9 | 1
  10 | 20
  11 | 220 11
  12 | 1760 264
  13 | 11440 3432 78

Mathematica

With[{q = 9}, 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 = 9

Crossrefs

Cf. A051288 (q=0), A213343 to A213350 (q=1 to 8), A213352 (q= 10).

Cf. A140354 (first column,with offset 9), A004315 (row sums).

Sequence in context: A141790 A229575 A125408 * A140236 A341371 A004411

Adjacent sequences: A213348 A213349 A213350 * A213352 A213353 A213354

Keyword

nonn,tabl

Author

Stanislav Sykora, Jun 13 2012

Status

approved