cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A213352 10-quantum transitions in systems of N >= 10 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

1, 22, 264, 12, 2288, 312, 16016, 4368, 91, 96096, 43680, 2730, 512512, 349440, 43680, 560, 2489344, 2376192, 495040, 19040, 11202048, 14257152, 4455360, 342720, 3060, 47297536, 77395968, 33860736, 4341120, 116280, 189190144, 386979840, 225738240, 43411200
Offset: 10

Views

Author

Stanislav Sykora, Jun 13 2012

Keywords

Comments

For a general discussion, please see A213343.
This a(n) is for decuple-quantum transitions (q = 10).
It lists the flattened triangle T(10;N,k) with rows N = 10,11,... and columns k = 0..floor((N-10)/2).

Examples

			Starting rows of the triangle:
   N | k = 0, 1, ..., floor((N-10)/2)
  ---+-------------------------------
  10 |     1
  11 |    22
  12 |   264   12
  13 |  2288  312
  14 | 16016 4368 91

References

Links

Crossrefs

Cf. A051288 (q=0), A213343 to A213351 (q=1 to 9).
Cf. A172242 (first column), A004316 (row sums).

Programs

  • Mathematica
    With[{q = 10}, 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 *)
  • PARI
    See A213343; set thisq = 10

Formula

Set q = 10 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

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

Original entry on oeis.org

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

Views

Author

Stanislav Sykora, Jun 09 2012

Keywords

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).

Examples

			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

References

Links

Crossrefs

Cf. A051288 (q=0), A213343 (q=1), A213345 to A213352 (q=3..10).
Cf. A001788 (first column), A002694 (row sums).

Programs

  • Mathematica
    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.

Formula

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

A213345 3-quantum transitions in systems of N>=3 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

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
Offset: 3

Views

Author

Stanislav Sykora, Jun 12 2012

Keywords

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).

Examples

			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

References

Links

Crossrefs

Cf. A051288 (q=0), A213343 (q=1), A213344 (q=2), A213346 to A213352 (q=4..10).
Cf. A001789 (first column), A002696 (row sums).

Programs

  • Mathematica
    With[{q = 3}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 13}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)
  • PARI
    See A213343; set thisq = 3.

Formula

Set q = 3 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

Views

Author

Stanislav Sykora, Jun 12 2012

Keywords

Comments

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).

Examples

			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

References

Links

Crossrefs

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).

Programs

  • Mathematica
    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

Formula

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

A213347 5-quantum transitions in systems of N>=5 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

1, 12, 84, 7, 448, 112, 2016, 1008, 36, 8064, 6720, 720, 29568, 36960, 7920, 165, 101376, 177408, 63360, 3960, 329472, 768768, 411840, 51480, 715, 1025024, 3075072, 2306304, 480480, 20020, 3075072, 11531520, 11531520
Offset: 5

Views

Author

Stanislav Sykora, Jun 13 2012

Keywords

Comments

For a general discussion, please see A213343.
This a(n) is for quintuple-quantum transitions (q = 5).
It lists the flattened triangle T(5;N,k) with rows N = 5,6,... and columns N, k = 0..floor((N-5)/2).

Examples

			Starting rows of the triangle:
  N | k = 0, 1, ..., floor((N-5)/2)
  5 |    1
  6 |   12
  7 |   84    7
  8 |  448  112
  9 | 2016 1008 36

References

Links

Crossrefs

Cf. A051288 (q=0), A213343 to A213346 (q=1 to 4), A213348 to A213352 (q=6 to 10).
A054849 (first column), A004311 (row sums).

Programs

  • Mathematica
    With[{q = 5}, Table[2^(n - q - 2 k)*Binomial[n, k] Binomial[n - k, q + k], {n, 15}, {k, 0, Floor[(n - q)/2]}]] // Flatten (* Michael De Vlieger, Nov 18 2019 *)
  • PARI
    See A213343; set thisq = 5

Formula

Set q = 5 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

A213348 6-quantum transitions in systems of N >= 6 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

1, 14, 112, 8, 672, 144, 3360, 1440, 45, 14784, 10560, 990, 59136, 63360, 11880, 220, 219648, 329472, 102960, 5720, 768768, 1537536, 720720, 80080, 1001, 2562560, 6589440, 4324320, 800800, 30030, 8200192, 26357760, 23063040
Offset: 6

Views

Author

Stanislav Sykora, Jun 13 2012

Keywords

Comments

For a general discussion, please see A213343.
This a(n) is for sextuple-quantum transitions (q = 6).
It lists the flattened triangle T(6;N,k) with rows N = 6,7,... and columns k = 0..floor((N-6)/2).

Examples

			Starting rows of the triangle:
   N | k = 0, 1, ..., floor((N-6)/2)
   6 |    1
   7 |   14
   8 |  112    8
   9 |  672  144
  10 | 3360 1440 45

References

Links

Crossrefs

Cf. A051288 (q=0), A213343 to A213347 (q=1 to 5), A213349 to A213352 (q=7 to 10).
Cf. A002409 (first column, with offset 6), A004312 (row sums).

Programs

  • Mathematica
    With[{q = 6}, 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 *)
  • PARI
    See A213343; set thisq = 6

Formula

Set q = 6 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

A213349 7-quantum transitions in systems of N >= 7 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

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
Offset: 7

Views

Author

Stanislav Sykora, Jun 13 2012

Keywords

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).

Examples

			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

References

Links

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).

Programs

  • 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 *)
  • PARI
    See A213343; set thisq = 7

Formula

Set q = 7 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).

A213350 8-quantum transitions in systems of N >= 8 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

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
Offset: 8

Views

Author

Stanislav Sykora, Jun 13 2012

Keywords

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).

Examples

			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

References

Links

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).

Programs

  • Mathematica
    With[{q = 8}, 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 *)
  • PARI
    See A213343; set thisq = 8

Formula

Set q = 8 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k)

A213351 9-quantum transitions in systems of N >= 9 spin 1/2 particles, in columns by combination indices.

Original entry on oeis.org

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
Offset: 9

Views

Author

Stanislav Sykora, Jun 13 2012

Keywords

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).

Examples

			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

References

Links

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).

Programs

  • 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 *)
  • PARI
    \\ See A213343; set thisq = 9

Formula

Set q = 9 in: T(q;N,k) = 2^(N-q-2*k)*binomial(N,k)*binomial(N-k,q+k).
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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