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A375873
A family of triangles T(m), m >= 0, read by triangles and then by rows; let P(m) be the triangle made up of the first m+1 rows of Pascal's triangle (A007318), R(m) (respectively L(m)) be P(m) rotated to the right (respectively to the left), T(m)(n, k) = gcd(P(m)(n, k), R(m)(n, k), L(m)(n, k)).
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
OFFSET
0,15
COMMENTS
T(m) has bilateral symmetry and 3-fold rotational symmetry.
LINKS
Rémy Sigrist, Colored representation of T(1023) (where the hue is function of T(1023)(n, k)).
Rémy Sigrist, Colored representation of T(1023) (where dark colors correspond to high values).
FORMULA
T(m)(n, k) = gcd(A007318(n, k), A007318(m-k, n-k), A007318(m-n+k, m-n)).
EXAMPLE
T(0) is:
1
T(1) is:
1
1 1
T(2) is:
1
1 1
1 1 1
T(3) is:
1
1 1
1 2 1
1 1 1 1
T(4) is:
1
1 1
1 1 1
1 1 1 1
1 1 1 1 1
T(5) is:
1
1 1
1 2 1
1 3 3 1
1 2 3 2 1
1 1 1 1 1 1
PROG
(PARI) T(m, n, k) = gcd([binomial(n, k), binomial(m-k, n-k), binomial(m-n+k, m-n)])
CROSSREFS
Sequence in context: A249770 A298481 A324872 * A307608 A323022 A284562
KEYWORD
nonn,tabf,easy
AUTHOR
Rémy Sigrist, Sep 01 2024
STATUS
approved