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A213345 3-quantum transitions in systems of N>=3 spin 1/2 particles, in columns by combination indices. 3
1, 8, 40, 5, 160, 60, 560, 420, 21, 1792, 2240, 336, 5376, 10080, 3024, 84, 15360, 40320, 20160, 1680, 42240, 147840, 110880, 18480, 330, 112640, 506880, 532224, 147840, 7920, 292864, 1647360, 2306304, 960960, 102960 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,2

COMMENTS

For a general discussion, please see A213343.

This a(n) is for triple-quantum transitions (q = 3).

It lists the flattened triangle T(3;N,k) with rows N = 3,5,... and columns k = 0..floor((N-3)/2).

REFERENCES

See A213343

LINKS

Stanislav Sykora, Table of n, a(n) for n = 3..2452

Stanislav Sykora, T(3;N,k) with rows N=3,..,100 and columns k=0,..,floor((N-3)/2)

FORMULA

Set q = 3 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

EXAMPLE

Some of the 40 triple-quantum transitions for N = 5 and combination index 0: (00000,01011),(10010,11111),...

Starting rows of the triangle T(3;N,k):

  N | k = 0, 1, ..., floor((N-3)/2)

  3 |   1

  4 |   8

  5 |  40   5

  6 | 160  60

  7 | 560 420 21

PROG

(PARI) See A213343; set thisq = 3.

CROSSREFS

Cf. A051288 (q=0), A213343 (q=1), A213344 (q=2), A213346 to A213352 (q=4..10).

Cf. A001789 (first column), A002696 (row sums).

Sequence in context: A264091 A154425 A120931 * A207360 A226904 A069083

Adjacent sequences:  A213342 A213343 A213344 * A213346 A213347 A213348

KEYWORD

tabf,nonn

AUTHOR

Stanislav Sykora, Jun 12 2012

STATUS

approved

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Last modified May 26 03:22 EDT 2017. Contains 287073 sequences.