|
|
A268918
|
|
Denominators of the rational number triangle R(m, a) = - a*(m - a)*(m - 2*a)/(6*m), m >= 1, a = 1, ..., m.
|
|
4
|
|
|
1, 1, 1, 9, 9, 1, 4, 1, 4, 1, 5, 5, 5, 5, 1, 9, 9, 1, 9, 9, 1, 7, 7, 7, 7, 7, 7, 1, 8, 1, 8, 1, 8, 1, 8, 1, 27, 27, 1, 27, 27, 1, 27, 27, 1, 5, 5, 5, 5, 1, 5, 5, 5, 5, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,4
|
|
COMMENTS
|
For details and the Hurwitz reference see A267863.
|
|
LINKS
|
|
|
FORMULA
|
T(m, a) = denominator(R(m, a)) with R(m, a) = - a*(m - a)*(m - 2*a)/(6*m), m >= 1, a = 1, ..., m.
|
|
EXAMPLE
|
The triangle T(m, a) begins:
m\a 1 2 3 4 5 6 7 8 9 10 11 12 ...
1: 1
2: 1 1
3: 9 9 1
4: 4 1 4 1
5: 5 5 5 5 1
6: 9 9 1 9 9 1
7: 7 7 7 7 7 7 1
8: 8 1 8 1 8 1 8 1
9: 27 27 1 27 27 1 27 27 1
10: 5 5 5 5 1 5 5 5 5 1
11: 11 11 11 11 11 11 11 11 11 11 1
12: 36 9 4 9 36 1 36 9 4 9 36 1
...
For the triangle of the rationals R(m, a) see A268917.
|
|
MATHEMATICA
|
Denominator@ Table[-a (m - a) (m - 2 a)/(6 m), {m, 12}, {a, m}] // Flatten (* Michael De Vlieger, Feb 26 2016 *)
|
|
PROG
|
(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(denominator(- k*(n-k)*(n-2*k)/(6*n)), ", "); ); print(); ); } \\ Michel Marcus, Feb 26 2016
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|