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

0,3

Comments

The numerators are given in A227984.

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

Links

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

Example

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.

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

Prog

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

Crossrefs

Cf. A000225, A213243, A213245, A227984.

Sequence in context: A348649 A010273 A046143 * A332538 A071812 A248133

Adjacent sequences: A228032 A228033 A228034 * A228036 A228037 A228038

Keyword

nonn,tabl,frac

Author

Vincenzo Librandi, Aug 12 2013

Status

approved