OFFSET
1,4
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n, k) = denominator(R(n, k)) with R(n, k) = - k*(n - k)*(n - 2*k)/(6*n), n >= 1, k = 1, ..., n.
EXAMPLE
The triangle T(n, k) begins:
n\k 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(n, k) see A268917.
MATHEMATICA
Denominator@ Table[-k (m - k) (m - 2 k)/(6 m), {m, 17}, {k, 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
(Magma)
A268918:= func< n, k | Denominator(k*(k-n)*(n-2*k)/(6*n)) >;
[A268918(n, k): k in [1..n], n in [1..17]]; // G. C. Greubel, Oct 04 2024
(SageMath)
def A268918(n, k): return denominator(k*(k-n)*(n-2*k)/(6*n))
flatten([[A268918(n, k) for k in range(1, n+1)] for n in range(1, 18)]) # G. C. Greubel, Oct 04 2024
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Feb 25 2016
EXTENSIONS
More terms added by G. C. Greubel, Oct 04 2024
STATUS
approved