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A356096
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; 2*t-u, 2*t-v; 2*u-t, t+u+v, 2*v-t; u, 2*u-v, 2*v-u, v].
4
1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, -1, 5, -1, 1, 1, 5, 5, 5, 5, 1, 1, -1, 5, 3, 5, -1, 1, 1, 1, 5, 5, 5, 5, 1, 1, 1, 3, 1, -1, 5, -1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, -1, 5, -1, 1
OFFSET
0,8
COMMENTS
We apply the following substitutions to transform T(m) into T(m+1):
t
/ \
/ \
t 2*t-u 2*t-v
/ \ ___\ / \ / \
/ \ / / \ / \
u-----v 2*u-t t+u+v 2*v-t
/ \ / \ / \
/ \ / \ / \
u---2*u-v--2*v-u--v
and:
u---2*u-v--2*v-u--v
\ / \ / \ /
\ / \ / \ /
u-----v 2*u-t t+u+v 2*v-t
\ / ___\ \ / \ /
\ / / \ / \ /
t 2*t-u 2*t-v
\ /
\ /
t
T(m) has 3^m+1 rows.
All terms are odd.
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
1 1
1 3 1
1 1 1 1
Triangle T(2) is:
1
1 1
1 3 1
1 1 1 1
1 -1 5 -1 1
1 5 5 5 5 1
1 -1 5 3 5 -1 1
1 1 5 5 5 5 1 1
1 3 1 -1 5 -1 1 3 1
1 1 1 1 1 1 1 1 1 1
PROG
(PARI) See Links section.
CROSSREFS
See A355855, A356002, A356097 and A356098 for similar sequences.
Sequence in context: A086997 A074298 A356097 * A326029 A356167 A176028
KEYWORD
sign,tabf
AUTHOR
Rémy Sigrist, Jul 26 2022
STATUS
approved