A213350 -id:A213350

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A213349

7-quantum transitions in systems of N >= 7 spin 1/2 particles, in columns by combination indices.

+10
3

1, 16, 144, 9, 960, 180, 5280, 1980, 55, 25344, 15840, 1320, 109824, 102960, 17160, 286, 439296, 576576, 160160, 8008, 1647360, 2882880, 1201200, 120120, 1365, 5857280, 13178880, 7687680, 1281280, 43680, 19914752, 56010240

(list; graph; refs; listen; history; text; internal format)

OFFSET

7,2

COMMENTS

For a general discussion, please see A213343.

This a(n) is for septuple-quantum transitions (q = 7).

It lists the flattened triangle T(7;N,k) with rows N = 7,8,... and columns k = 0..floor((N-7)/2).

REFERENCES

See A213343

LINKS

Stanislav Sykora, Table of n, a(n) for n = 7..2262

Stanislav Sykora, T(7;N,k) with rows N = 7..100 and columns k = 0..floor((N-7)/2)

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

FORMULA

Set q = 7 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-7)/2)

7 | 1

8 | 16

9 | 144 9

10 | 960 180

11 | 5280 1980 55

MATHEMATICA

With[{q = 7}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, q, q + 10}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 20 2019 *)

PROG

(PARI) See A213343; set thisq = 7

CROSSREFS

Cf. A051288 (q=0), A213343 to A213348 (q=1 to 6), A213350 to A213352 (q=8 to 10).

Cf. A054851 (first column), A004313 (row sums).

KEYWORD

nonn,tabf

AUTHOR

Stanislav Sykora, Jun 13 2012

STATUS

approved

A213351

9-quantum transitions in systems of N >= 9 spin 1/2 particles, in columns by combination indices.

+10
3

1, 20, 220, 11, 1760, 264, 11440, 3432, 78, 64064, 32032, 2184, 320320, 240240, 32760, 455, 1464320, 1537536, 349440, 14560, 6223360, 8712704, 2970240, 247520, 2380, 24893440, 44808192, 21385728, 2970240, 85680, 94595072, 212838912, 135442944, 28217280

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

9,2

COMMENTS

For a general discussion, please see A213343.

This a(n) is for nonuple-quantum transitions (q = 9).

It lists the flattened triangle T(9;N,k) with rows N = 9,10,... and columns k = floor((N-9)/2).

REFERENCES

See A213343

LINKS

Stanislav Sykora, Table of n, a(n) for n = 9..2170

Stanislav Sykora, T(9;N,k) with rows N = 9..100 and columns k = 0..floor((N-9)/2)

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

FORMULA

Set q = 9 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-9)/2)

---+------------------------------

9 | 1

10 | 20

11 | 220 11

12 | 1760 264

13 | 11440 3432 78

MATHEMATICA

With[{q = 9}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, q, q + 10}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 20 2019 *)

PROG

(PARI) See A213343; set thisq = 9

CROSSREFS

Cf. A051288 (q=0), A213343 to A213350 (q=1 to 8), A213352 (q= 10).

Cf. A140354 (first column,with offset 9), A004315 (row sums).