A213345 -id:A213345 - cp's OEIS frontend

A213344 2-quantum transitions in systems of N>=2 spin 1/2 particles, in columns by combination indices.

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

Offset: 2

Stanislav Sykora, Jun 09 2012

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).

			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

See A213343.

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

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

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

With[{q = 2}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 12}, {k, 0, Floor[(n - 2)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

PARI
```
See A213343; set thisq = 2.
```

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

A213346 4-quantum transitions in systems of N>=4 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

1, 10, 60, 6, 280, 84, 1120, 672, 28, 4032, 4032, 504, 13440, 20160, 5040, 120, 42240, 88704, 36960, 2640, 126720, 354816, 221760, 31680, 495, 366080, 1317888, 1153152, 274560, 12870, 1025024, 4612608, 5381376, 1921920, 180180, 2002

Offset: 4

Stanislav Sykora, Jun 12 2012

For a general discussion, please see A213343.
This a(n) is for quadruple-quantum transitions (q = 4).
It lists the flattened triangle T(4;N,k) with rows N = 4,5,... and columns k = 0..floor((N-4)/2).

			Starting rows of the triangle:
  N | k = 0, 1, ..., floor((N-4)/2)
  4 |    1
  5 |   10
  6 |   60   6
  7 |  280  84
  8 | 1120 672 28

See A213343.

Stanislav Sykora, Table of n, a(n) for n = 4..2404
Stanislav Sykora, T(4;N,k) with rows N=4,..,100 and columns k=0,..,floor((N-4)/2)
Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.

Cf. A051288 (q=0), A213343 to A213345 (q=1 to 3), A213347 to A213352 (q=5 to 10).

Cf. A003472 (first column), A004310 (row sums).

With[{q = 4}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 14}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)

PARI
```
See A213343; set thisq = 4
```

Set q = 4 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k)

cp's OEIS Frontend

A213344 2-quantum transitions in systems of N>=2 spin 1/2 particles, in columns by combination indices.

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