The On-Line Encyclopedia of Integer Sequences (OEIS)

A213350 revision #11

A213350

8-quantum transitions in systems of N>=8 spin 1/2 particles, in columns by combination indices.

1, 18, 180, 10, 1320, 220, 7920, 2640, 66, 41184, 22880, 1716, 192192, 160160, 24024, 364, 823680, 960960, 240240, 10920, 3294720, 5125120, 1921920, 174720, 1820, 12446720, 24893440, 13069056, 1980160, 61880, 44808192, 112020480

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OFFSET

8,2

COMMENTS

For a general discussion, please see A213343.

This a(n) is for octuple-quantum transitions (q = 8).

It lists the flattened triangle T(8;N,k) with rows N = 8,9,... and columns k = 0,..,floor((N-8)/2).

REFERENCES

See A213343

LINKS

Stanislav Sykora, Table of n, a(n) for n = 8..2216

Stanislav Sykora, T(8;N,k) with rows N=8,..,100 and columns k=0,..,floor((N-8)/2)

FORMULA

Set q = 8 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-8)/2)

8 | 1

9 | 18

10 | 180 10

11 | 1320 220

12 | 7920 2640 66

PROG

(PARI) See A213343; set thisq = 8

CROSSREFS

Cf. A051288 (q=0), A213343 to A213349 (q=1 to 7), A213351 (q=9), A213352 (q= 10).

Cf. A140325 (first row, with offset 8), A004314 (row sums).

Sequence in context: A321951 A227023 A239581 * A052507 A071910 A121038

Adjacent sequences: A213347 A213348 A213349 * A213351 A213352 A213353

KEYWORD

nonn,tabl

AUTHOR

Stanislav Sykora, Jun 13 2012

STATUS

editing