A213352 10-quantum transitions in systems of N >= 10 spin 1/2 particles, in columns by combination indices.

1, 22, 264, 12, 2288, 312, 16016, 4368, 91, 96096, 43680, 2730, 512512, 349440, 43680, 560, 2489344, 2376192, 495040, 19040, 11202048, 14257152, 4455360, 342720, 3060, 47297536, 77395968, 33860736, 4341120, 116280, 189190144, 386979840, 225738240, 43411200

Offset

10,2

Comments

For a general discussion, please see A213343.

This a(n) is for decuple-quantum transitions (q = 10).

It lists the flattened triangle T(10;N,k) with rows N = 10,11,... and columns k = 0..floor((N-10)/2).

References

See A213343.

Links

Stanislav Sykora, Table of n, a(n) for n = 10..2125

Stanislav Sykora, T(10;N,k) with rows N=10..100 and columns k=0..floor((N-10)/2)

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

Formula

Set q = 10 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-10)/2)
  ---+-------------------------------
  10 |     1
  11 |    22
  12 |   264   12
  13 |  2288  312
  14 | 16016 4368 91

Mathematica

With[{q = 10}, 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 = 10

Crossrefs

Cf. A051288 (q=0), A213343 to A213351 (q=1 to 9).

Cf. A172242 (first column), A004316 (row sums).

Sequence in context: A010974 A022587 A143479 * A004412 A172242 A055756

Adjacent sequences: A213349 A213350 A213351 * A213353 A213354 A213355

Keyword

nonn,tabl

Author

Stanislav Sykora, Jun 13 2012

Status

approved