A268918 Denominators of the rational number triangle R(m, a) = - a*(m - a)*(m - 2*a)/(6*m), m >= 1, a = 1, ..., m.

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

Offset

1,4

Comments

For the numerators see A268917.

For details and the Hurwitz reference see A267863.

Links

Table of n, a(n) for n=1..55.

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

Cf. A268917.

Sequence in context: A280554 A195722 A133627 * A144982 A228788 A019788

Adjacent sequences: A268915 A268916 A268917 * A268919 A268920 A268921

Keyword

nonn,frac,tabl,easy

Author

Wolfdieter Lang, Feb 25 2016

Status

approved