A268918 - OEIS

%I #16 Oct 05 2024 09:40:28

%S 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,

%T 8,1,27,27,1,27,27,1,27,27,1,5,5,5,5,1,5,5,5,5,1,11,11,11,11,11,11,11,

%U 11,11,11,1,36,9,4,9,36,1,36,9,4,9,36,1,13,13,13,13,13,13,13,13,13,13,13,13,1,7,7,7,7,7,7,1,7,7,7,7,7,7,1

%N Denominators of the rational number triangle R(n, k) = - k*(n - k)*(n - 2*k)/(6*n), n >= 1, k = 1, ..., n.

%C For the numerators see A268917.

%C For details and the Hurwitz reference see A267863.

%H G. C. Greubel, <a href="/A268918/b268918.txt">Rows n = 1..50 of the triangle, flattened</a>

%F T(n, k) = denominator(R(n, k)) with R(n, k) = - k*(n - k)*(n - 2*k)/(6*n), n >= 1, k = 1, ..., n.

%e The triangle T(n, k) begins:

%e   n\k   1  2  3  4  5  6  7  8  9 10  11  12 ...

%e   1:    1

%e   2:    1  1

%e   3:    9  9  1

%e   4:    4  1  4  1

%e   5:    5  5  5  5  1

%e   6:    9  9  1  9  9  1

%e   7:    7  7  7  7  7  7  1

%e   8:    8  1  8  1  8  1  8  1

%e   9:   27 27  1 27 27  1 27 27  1

%e   10:   5  5  5  5  1  5  5  5  5  1

%e   11:  11 11 11 11 11 11 11 11 11 11   1

%e   12:  36  9  4  9 36  1 36  9  4  9  36   1

%e   ...

%e For the triangle of the rationals R(n, k) see A268917.

%t Denominator@ Table[-k (m - k) (m - 2 k)/(6 m), {m, 17}, {k, m}] // Flatten (* _Michael De Vlieger_, Feb 26 2016 *)

%o (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

%o (Magma)

%o A268918:= func< n,k | Denominator(k*(k-n)*(n-2*k)/(6*n)) >;

%o [A268918(n,k): k in [1..n], n in [1..17]]; // _G. C. Greubel_, Oct 04 2024

%o (SageMath)

%o def A268918(n,k): return denominator(k*(k-n)*(n-2*k)/(6*n))

%o flatten([[A268918(n,k) for k in range(1,n+1)] for n in range(1,18)]) # _G. C. Greubel_, Oct 04 2024

%Y Cf. A268917.

%K nonn,frac,tabl,easy

%O 1,4

%A _Wolfdieter Lang_, Feb 25 2016

%E More terms added by _G. C. Greubel_, Oct 04 2024