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 1-5 of 5 results.

A060963 Number of pairings of the first 2n positive integers so that the absolute differences of each pair are different.

Original entry on oeis.org

1, 1, 1, 5, 29, 145, 957, 8397, 85169, 944221, 11639417, 160699437, 2430145085, 39776366397, 703161838717, 13369111112753, 271734091323897
Offset: 0

Views

Author

Erich Friedman, May 08 2001

Keywords

Comments

Number of perfect Skolem-type sequences.

Examples

			a(3)=5 since the 5 pairings of {1, 2, 3, 4, 5, 6} are {1, 3} {2, 6} {4, 5}, {1, 5} {2, 3} {4, 6}, {1, 5} {2, 4} {3, 6}, {1, 4} {2, 6} {3, 5}, {1, 6} {2, 5} {3, 4}.

Links

Crossrefs

Cf. A261516, A261517, A322178.

Extensions

Offset corrected by Alois P. Heinz, Sep 14 2015
a(14) from Fausto A. C. Cariboni, Mar 03 2017
a(15) from Fausto A. C. Cariboni, Apr 10 2017
a(16) from Edward Moody, Feb 17 2020

A261517 Number of perfect rhythmic tilings of [0,4n-1] with quadruplets.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 24, 38, 96, 444, 1414, 5134, 19490
Offset: 0

Views

Author

Michel Marcus, Aug 23 2015

Keywords

Comments

A perfect tiling of the line with quadruplets consists of groups of four evenly spaced points, each group having a different common interval such that all points of the line are covered.

Examples

			For n=1, there is 1 such tiling: (0,1,2,3).
For n=15, there are 2 such tilings: [0, 16, 32, 48], [1, 3, 5, 7], [2, 13, 24, 35], [4, 22, 40, 58], [6, 21, 36, 51], [8, 14, 20, 26], [9, 10, 11, 12], [15, 29, 43, 57], [17, 25, 33, 41], [18, 30, 42, 54], [19, 23, 27, 31], [28, 37, 46, 55], [34, 39, 44, 49], [38, 45, 52, 59], [47, 50, 53, 56] and its mirror (see Ekhad et al. link).

References

  • J. P. Delahaye, La musique mathématique de Tom Johnson, in Mathématiques pour le plaisir, Belin-Pour la Science, Paris, 2010.

Links

Crossrefs

Cf. A060963, A261516.

Extensions

a(21)-a(23) from Fausto A. C. Cariboni, Mar 18 2017
a(0)=1 prepended by Seiichi Manyama, Feb 22 2020

A285527 Number of super perfect rhythmic tilings of [0,3n-1] with triples.

Original entry on oeis.org

1, 1, 0, 0, 0, 0, 0, 0, 0, 18, 40, 66, 0, 0, 0, 0, 0, 0, 400686, 1738012, 8495580, 0, 0, 0, 0, 0, 0
Offset: 0

Views

Author

Tony Reix, Apr 20 2017

Keywords

Comments

A super perfect tiling of the line with triples consists of n groups of three evenly spaced points, each group having a different common interval such that all points of the line are covered, and such that all intervals are inferior or equal to n (thus, each interval belongs to [1..n]).

Examples

			For n = 9, there are 18 tilings.
One is: (0,2,4), (1,5,9), (3,11,19), (6,12,18), (7,14,21), (8,17,26), (10,13,16), (15,20,25), (22,23,24), with the intervals: 1,2,3,4,5,6,7,8,9 appearing in order: 2,4,8,6,7,9,3,5,1.
It can also be represented as:
2 4 2 8 2 4 6 7 9 4 3 8 6 3 7 5 3 9 6 8 5 7 1 1 1 5 9

Crossrefs

Cf. A261516, A320392.

Formula

For n>1, a(n) = A059108(n)*2 because A059108 ignores reflected solutions. - Fausto A. C. Cariboni, May 20 2017

A332748 The number of permutations of {1,1,1,2,2,2,...,n,n,n} such that each triple of k's (k=1..n) is equally spaced with b(k) other elements in between and b(1) >= b(2) >= ... >= b(n).

Original entry on oeis.org

1, 1, 4, 18, 124, 738, 7464, 55890, 668778, 7030210, 90713844, 1054221258, 18597735744, 242795838520
Offset: 0

Views

Author

Seiichi Manyama, Feb 21 2020

Keywords

Examples

			n = 1 case:
     |           | b(1)
-----+-----------+------
   1 | [1, 1, 1] | [0] *
.
n = 2 case:
     |                    | b(1),b(2)
-----+--------------------+----------
   1 | [2, 2, 2, 1, 1, 1] | [0, 0]
   2 | [2, 1, 2, 1, 2, 1] | [1, 1]
   3 | [1, 2, 1, 2, 1, 2] | [1, 1]
   4 | [1, 1, 1, 2, 2, 2] | [0, 0]
.
n = 3 case:
     |                             | b(1),b(2),b(3)
-----+-----------------------------+---------------
   1 | [3, 3, 3, 2, 2, 2, 1, 1, 1] | [0, 0, 0]
   2 | [3, 3, 3, 2, 1, 2, 1, 2, 1] | [1, 1, 0]
   3 | [3, 3, 3, 1, 2, 1, 2, 1, 2] | [1, 1, 0]
   4 | [3, 3, 3, 1, 1, 1, 2, 2, 2] | [0, 0, 0]
   5 | [3, 2, 1, 3, 2, 1, 3, 2, 1] | [2, 2, 2]
   6 | [3, 1, 2, 3, 1, 2, 3, 1, 2] | [2, 2, 2]
   7 | [1, 3, 3, 3, 1, 2, 2, 2, 1] | [3, 0, 0]
   8 | [2, 3, 1, 2, 3, 1, 2, 3, 1] | [2, 2, 2]
   9 | [1, 3, 2, 1, 3, 2, 1, 3, 2] | [2, 2, 2]
  10 | [2, 1, 3, 2, 1, 3, 2, 1, 3] | [2, 2, 2]
  11 | [1, 2, 3, 1, 2, 3, 1, 2, 3] | [2, 2, 2]
  12 | [2, 2, 2, 3, 3, 3, 1, 1, 1] | [0, 0, 0]
  13 | [1, 1, 1, 3, 3, 3, 2, 2, 2] | [0, 0, 0]
  14 | [1, 2, 2, 2, 1, 3, 3, 3, 1] | [3, 0, 0]
  15 | [2, 2, 2, 1, 1, 1, 3, 3, 3] | [0, 0, 0]
  16 | [2, 1, 2, 1, 2, 1, 3, 3, 3] | [1, 1, 0]
  17 | [1, 2, 1, 2, 1, 2, 3, 3, 3] | [1, 1, 0]
  18 | [1, 1, 1, 2, 2, 2, 3, 3, 3] | [0, 0, 0]
* (strongly decreasing)

Crossrefs

Column k=3 of A332762.
Cf. A104429, A059108, A261516 (strongly decreasing), A322178, A332752.

Extensions

a(10)-a(13) from Max Alekseyev, Sep 26 2023

A264813 Number of permutations of 3 indistinguishable copies of 1,...,n such that the first and second copies of j are adjacent and there are exactly j numbers between the second and the third copy of j.

Original entry on oeis.org

1, 0, 1, 1, 0, 3, 6, 0, 53, 199, 0, 2908, 13699, 0, 369985, 2135430, 0, 87265700, 611286653, 0
Offset: 0

Views

Author

Alois P. Heinz, Nov 25 2015

Keywords

Comments

a(n) = 0 for n == 1 (mod 3).

Examples

			a(0) = 1: the empty permutation.
a(2) = 1: 221121.
a(3) = 1: 223321131.
a(5) = 3: 223325534411514, 225523344531141, 552244253341131.
a(6) = 6: 221121665544336543, 225523366534411614, 225526633544361141, 446611415563322532, 552266253344631141, 665544336543221121.

Links

Crossrefs

Cf. A014552, A104185, A108235, A176127, A203435, A261516, A261517, A321956.
Showing 1-5 of 5 results.

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

Content is available under The OEIS End-User License Agreement.