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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.

User: Tony Reix

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Tony Reix has authored 2 sequences.

A285698 Number of super perfect rhythmic tilings of [0,4n-1] with quadruples.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 110, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Tony Reix, Apr 25 2017

Keywords

Comments

A super perfect tiling of the line with quadruples consists of n groups of four 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 = 24, there are 20 tilings.
One is: (0,3,6,9), (1,7,13,19), (2,14,26,38), (4,11,18,25), (5,29,53,77), (8,12,16,20), (10,27,44,61), (15,37,59,81), (17,33,49,65), (21,36,51,66), (22,43,64,85), (23,34,45,56), (24,47,70,93), (28,41,54,67), (30,39,48,57), (31,50,69,88), (32,46,60,74), (35,55,75,95), (40,58,76,94), (42,52,62,72), (63,71,79,87), (68,73,78,83), (80,82,84,86), (89,90,91,92)
It can also be represented as (where each number is the interval of the group the point of the line belongs to):
3 6 12 3 7 24 3 6 4 3 17 7 4 6 12 22 4 16 7 6 4 15 21 11 23 7 12 17 13 24 9 19 14 16 11 20 15 22 12 9 18 13 10 21 17 11 14 23 9 16 19 15 10 24 13 20 11 9 18 22 14 17 10 8 21 16 15 13 5 19 23 8 10 5 14 20 18 24 5 8 2 22 2 5 2 21 2 8 19 1 1 1 1 23 18 20
Another one is: (0,23,46,69), (1,25,49,73), (2,4,6,8), (3,7,11,15), (5,26,47,68), (9,14,19,24), (10,27,44,61), (12,20,28,36), (13,35,57,79), (16,34,52,70), (17,31,45,59), (18,33,48,63), (21,32,43,54), (22,42,62,82), (29,41,53,65), (30,40,50,60), (37,56,75,94), (38,51,64,77), (39,55,71,87), (58,67,76,85), (66,72,78,84), (74,81,88,95), (80,83,86,89), (90,91,92,93)
It can also be represented as:
23 24 2 4 2 21 2 4 2 5 17 4 8 22 5 4 18 14 15 5 8 11 20 23 5 24 21 17 8 12 10 14 11 15 18 22 8 19 13 16 10 12 20 11 17 14 23 21 15 24 10 13 18 12 11 16 19 22 9 14 10 17 20 15 13 12 6 9 21 23 18 16 6 24 7 19 9 13 6 22 3 7 20 3 6 9 3 16 7 3 1 1 1 1 19 7

Crossrefs

Cf. A285527, A261517.

Formula

For n > 1, a(n) = A284757(n)*2 because A284757 ignores reflected solutions. - Fausto A. C. Cariboni, May 20 2017
a(n) = 0 if (n mod 8) not in {0, 1}, - Max Alekseyev, Sep 28 2023

Extensions

a(27)-a(31) from Max Alekseyev, Sep 24 2023

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

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