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A213346
4-quantum transitions in systems of N>=4 spin 1/2 particles, in columns by combination indices.
3
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
4,2
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).
REFERENCES
See A213343.
LINKS
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
FORMULA
Set q = 4 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-4)/2)
4 | 1
5 | 10
6 | 60 6
7 | 280 84
8 | 1120 672 28
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 *)
PROG
(PARI) See A213343; set thisq = 4
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).
Sequence in context: A054489 A219580 A267021 * A140890 A055714 A046762
KEYWORD
tabl,nonn
AUTHOR
Stanislav Sykora, Jun 12 2012
STATUS
approved