A228035 Triangle T(n,k), read by rows: T(n,k) is the denominator of (1-2^(n-k+1))/(1-2^(k+1)).

1, 1, 3, 1, 1, 7, 1, 3, 7, 15, 1, 1, 1, 5, 31, 1, 3, 7, 15, 31, 63, 1, 1, 7, 1, 31, 21, 127, 1, 3, 1, 15, 31, 9, 127, 255, 1, 1, 7, 5, 1, 21, 127, 85, 511, 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 1, 1, 1, 1, 31, 1, 127, 17, 73, 341, 2047, 1, 3, 7, 15, 31, 63

Offset: 0

Author

Vincenzo Librandi, Aug 12 2013

Keywords

• nonn
• tabl
• frac

Comments

The numerators are given in A227984.

The first diagonal is A000225, the second diagonal is A213243, the third diagonal is A213245.

Examples

			Triangle begins:
1;
1, 3;
1, 1, 7;
1, 3, 7, 15;
1, 1, 1, 5,  31;
1, 3, 7, 15, 31, 63;
1, 1, 7, 1,  31, 21, 127;
1, 3, 1, 15, 31, 9,  127, 255;
1, 1, 7, 5,  1,  21, 127, 85,  511;
1, 3, 7, 15, 31, 63, 127, 255, 511, 1023;
1, 1, 1, 1,  31, 1,  127, 17,  73,  341, 2047; etc.
		

Links

• Vincenzo Librandi, Rows n = 0..100, flattened

Crossrefs

Cf. A000225, A213243, A213245, A227984.

Programs

Magma

[Denominator((1-2^(n-k+1))/(1-2^(k+1))): k in [0..n], n in [0..11]];

Mathematica

a[n_, k_] := Denominator[(1 - 2^(n - k + 1))/(1 - 2^(k + 1))];
Table[a[n, k], {n, 0, 11}, {k, 0, n}] // Flatten