|
|
A375388
|
|
A family of squares S(m), m > 0, read by squares and then by rows; square S(1) is [1, 1; 1, 1]; for m > 0, square S(m+1) is obtained by replacing each subsquare [t, u; v, w] in S(m) by [t, t+u, u; t+v, t+u+v+w, u+w; v, v+w, w].
|
|
1
|
|
|
1, 1, 1, 1, 1, 2, 1, 2, 4, 2, 1, 2, 1, 1, 3, 2, 3, 1, 3, 9, 6, 9, 3, 2, 6, 4, 6, 2, 3, 9, 6, 9, 3, 1, 3, 2, 3, 1, 1, 4, 3, 5, 2, 5, 3, 4, 1, 4, 16, 12, 20, 8, 20, 12, 16, 4, 3, 12, 9, 15, 6, 15, 9, 12, 3, 5, 20, 15, 25, 10, 25, 15, 20, 5, 2, 8, 6, 10, 4, 10, 6, 8, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,6
|
|
COMMENTS
|
We apply the following substitutions to transform S(m) into S(m+1):
t----t+u----u
| | |
t--u | t+u |
| | --> t+v----+----u+w
v--w | v+w |
| | |
v----v+w----w
This sequence can be seen as a two-dimensional variant of A049456.
The base of T(m) corresponds to the m-th row of A049456.
As A355855, this sequence is related to nonperiodic tilings based on tiles decorated with elements of F_p for some odd prime number p; here we use square tiles, there triangular tiles.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
S(1) is:
1 1
1 1
S(2) is:
1 2 1
2 4 2
1 2 1
S(3) is:
1 3 2 3 1
3 9 6 9 3
2 6 4 6 2
3 9 6 9 3
1 3 2 3 1
S(4) is:
1 4 3 5 2 5 3 4 1
4 16 12 20 8 20 12 16 4
3 12 9 15 6 15 9 12 3
5 20 15 25 10 25 15 20 5
2 8 6 10 4 10 6 8 2
5 20 15 25 10 25 15 20 5
3 12 9 15 6 15 9 12 3
4 16 12 20 8 20 12 16 4
1 4 3 5 2 5 3 4 1
|
|
PROG
|
(PARI) S(n) = { matrix(2^(n-1)+1, 2^(n-1)+1, i, j, A002487(2^(n-1)-1+i) * A002487(2^(n-1)-1+j)); }
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf,new
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|