OFFSET
1,24
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]).
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
EXAMPLE
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
KEYWORD
nonn,more
AUTHOR
Tony Reix, Apr 25 2017
EXTENSIONS
a(27)-a(31) from Max Alekseyev, Sep 24 2023
STATUS
approved