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A213344 2-quantum transitions in systems of N>=2 spin 1/2 particles, in columns by combination indices. 3
1, 6, 24, 4, 80, 40, 240, 240, 15, 672, 1120, 210, 1792, 4480, 1680, 56, 4608, 16128, 10080, 1008, 11520, 53760, 50400, 10080, 210, 28160, 168960, 221760, 73920, 4620, 67584, 506880, 887040, 443520, 55440, 792 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

COMMENTS

For a general discussion, please see A213343.

This a(n) is for double-quantum transitions (q = 2).

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

REFERENCES

See A213343.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 2..2501

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

FORMULA

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

EXAMPLE

For N=4, there are 4 second-quantum transitions with combination index 1: (0001,1110),(0010,1101),(0100,1011),(1000,0111).

Starting rows of the triangle:

  N | k = 0, 1, ..., floor((N-2)/2)

  2 |   1

  3 |   6

  4 |  24   4

  5 |  80  40

  6 | 240 240 15

PROG

(PARI) See A213343; set thisq = 2.

CROSSREFS

Cf. A051288 (q=0), A213343 (q=1), A213345 to A213352 (q=3..10).

Cf. A001788 (first column), A002694 (row sums).

Sequence in context: A255305 A194770 A052697 * A193429 A213278 A029592

Adjacent sequences:  A213341 A213342 A213343 * A213345 A213346 A213347

KEYWORD

nonn,tabf

AUTHOR

Stanislav Sykora, Jun 09 2012

STATUS

approved

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Last modified May 22 16:19 EDT 2017. Contains 286882 sequences.