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A213347 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices. 3
1, 12, 84, 7, 448, 112, 2016, 1008, 36, 8064, 6720, 720, 29568, 36960, 7920, 165, 101376, 177408, 63360, 3960, 329472, 768768, 411840, 51480, 715, 1025024, 3075072, 2306304, 480480, 20020, 3075072, 11531520, 11531520 (list; graph; refs; listen; history; text; internal format)
OFFSET

5,2

COMMENTS

For a general discussion, please see A213343.

This a(n) is for quintuple-quantum transitions (q = 5).

It lists the flattened triangle T(5;N,k) with rows N = 5,6,... and columns N, k = 0..floor((N-5)/2).

REFERENCES

See A213343

LINKS

Stanislav Sykora, Table of n, a(n) for n = 5..2356

Stanislav Sykora, T(5;N,k) with rows N=5,..,100 and columns k=0,..,floor((N-5)/2)

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

FORMULA

Set q = 5 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-5)/2)

  5 |    1

  6 |   12

  7 |   84    7

  8 |  448  112

  9 | 2016 1008 36

MATHEMATICA

With[{q = 5}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 15}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

PROG

(PARI) See A213343; set thisq = 5

CROSSREFS

Cf. A051288 (q=0), A213343 to A213346 (q=1 to 4), A213348 to A213352 (q=6 to 10).

A054849 (first column), A004311 (row sums).

Sequence in context: A275743 A026949 A165127 * A075476 A298977 A213784

Adjacent sequences:  A213344 A213345 A213346 * A213348 A213349 A213350

KEYWORD

tabf,nonn

AUTHOR

Stanislav Sykora, Jun 13 2012

STATUS

approved

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Last modified May 26 08:39 EDT 2020. Contains 334620 sequences. (Running on oeis4.)