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URL: https://oeis.org/A356098

⇱ A356098 - OEIS

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A356098
A family of triangles T(m), m >= 0, read by triangles and then by rows; triangle T(0) is [1; 1, 1]; for m >= 0, triangle T(m+1) is obtained by replacing each subtriangle [t; u, v] in T(m) by [t; t-u, t-v; u-t, t+u+v, v-t; u, u-v, v-u, v].
4
1, 1, 1, 1, 0, 0, 0, 3, 0, 1, 0, 0, 1, 1, 1, 1, -1, 1, -1, 0, 0, 0, 0, 0, -3, 3, -3, 0, 0, 3, 3, 3, 3, 0, 0, -3, 3, 3, 3, -3, 0, -1, 0, 3, 3, 3, 3, 0, -1, 1, 1, 0, -3, 3, -3, 0, 1, 1, 1, 1, -1, 0, 0, 0, 0, -1, 1, 1, 1, 0, 0, 0, 3, 0, 1, 0, 0, 1, 2, 0, 3, 0, 2
OFFSET
0,8
COMMENTS
We apply the following substitutions to transform T(m) into T(m+1):
t
/ \
/ \
t t-u---t-v
/ \ ___\ / \ / \
/ \ / / \ / \
u-----v u-t--t+u+v--v-t
/ \ / \ / \
/ \ / \ / \
u----u-v---v-u----v
and:
u----u-v---v-u----v
\ / \ / \ /
\ / \ / \ /
u-----v u-t--t+u+v--v-t
\ / ___\ \ / \ /
\ / / \ / \ /
t t-u---t-v
\ /
\ /
t
T(m) has 3^m+1 rows.
As m gets larger, T(m) exhibits interesting fractal features (see illustrations in Links section).
EXAMPLE
Triangle T(0) is:
1
1 1
Triangle T(1) is:
1
0 0
0 3 0
1 0 0 1
Triangle T(2) is:
1
1 1
-1 1 -1
0 0 0 0
0 -3 3 -3 0
0 3 3 3 3 0
0 -3 3 3 3 -3 0
-1 0 3 3 3 3 0 -1
1 1 0 -3 3 -3 0 1 1
1 1 -1 0 0 0 0 -1 1 1
PROG
(PARI) See Links section.
CROSSREFS
See A355855, A356002, A356096 and A356097 for similar sequences.
Sequence in context: A196306 A107093 A051830 * A106216 A035676 A369283
KEYWORD
sign,tabl
AUTHOR
Rémy Sigrist, Jul 26 2022
STATUS
approved