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 1-4 of 4 results.

A001627 Related to Latin rectangles.

Original entry on oeis.org

1, 0, 2, 44, 1008, 34432, 1629280, 101401344, 8030787968, 788377273856, 93933191303424, 13350759115563520, 2231133728986759168, 433075048506207645696, 96617322164029448916992, 24549315871469898190266368, 7047652261245574026565877760
Offset: 1

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Keywords

References

  • S. M. Kerawala, The enumeration of the Latin rectangle of depth three by means of a difference equation, Bull. Calcutta Math. Soc., 33 (1941), 119-127.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Formula

a(1) = 1, a(n) = A000186(n) + A000186(n-1) + 3*(n-1)*A001626(n-1). - Sean A. Irvine, Sep 25 2015

Extensions

More terms from Sean A. Irvine, Sep 25 2015

A001624 Related to Latin rectangles.

Original entry on oeis.org

1, 5, 58, 1274, 41728, 1912112, 116346400, 9059742176, 877746364288, 103483282967936, 14581464284095744, 2419278174185319680, 466730664414683625472, 103580258158369503481856, 26198788829773597178540032
Offset: 2

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Author

Keywords

References

  • S. M. Kerawala, The enumeration of the Latin rectangle of depth three by means of a difference equation, Bull. Calcutta Math. Soc., 33 (1941), 119-127.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Formula

a(2) = 1, a(n) = A001626(n) + A001626(n-1) + A001627(n-1) + (n-2)(a(n-1) + A001625(n-1)). - Sean A. Irvine, Sep 25 2015

Extensions

More terms from Sean A. Irvine, Sep 25 2015

A001625 Related to Latin rectangles.

Original entry on oeis.org

2, 4, 60, 1276, 41888, 1916064, 116522048, 9069595840, 878460379392, 103547791177216, 14588580791234048, 2420219602973093376, 466877775127725240320, 103607067936116866084864, 26204424894484840874483712
Offset: 2

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Author

Keywords

References

  • S. M. Kerawala, The enumeration of the Latin rectangle of depth three by means of a difference equation, Bull. Calcutta Math. Soc., 33 (1941), 119-127.
  • N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
  • N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Formula

a(2) = 2, a(n) = A001626(n) + 2 * A001627(n-1) + 2 * (n-1) * A001624(n-1). - Sean A. Irvine, Sep 25 2015

Extensions

More terms from Sean A. Irvine, Sep 25 2015

A347927 a(n) is the number of reduced Latin trapezoids of height 3, whose top row has n boxes, the middle row has n+1 boxes, and the bottom row has n+2 boxes.

Original entry on oeis.org

1, 6, 68, 1670, 67295, 3825722, 285667270, 26889145828, 3102187523467, 429700007845870, 70303573947346474, 13405343287124139802, 2945521072579394529097, 738633749151050116349946, 209620243382776121032416188, 66830750007674204750148252472, 23780886787936166425634118631117
Offset: 1

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Author

Peter Luschny, Oct 22 2021

Keywords

Examples

			There are 6 reduced Latin trapezoids of height 3 with base of length 4:
----------------------------------------------
    2, 3;       |    4, 3;       |    2, 3;
   3, 1, 2;     |   3, 1, 2;     |   3, 4, 1;
  1, 2, 3, 4;   |  1, 2, 3, 4;   |  1, 2, 3, 4;
-----------------------------------------------
    2, 1;       |    2, 3;       |    2, 3;
   3, 4, 2;     |   3, 4, 2;     |   4, 1, 2;
  1, 2, 3, 4;   |  1, 2, 3, 4;   |  1, 2, 3, 4;
-----------------------------------------------
		

Crossrefs

Cf. A002860 (Latin squares), A000186, A001623, A001626.
Showing 1-4 of 4 results.