A227984 Triangle T(n,k), read by rows: T(n,k) is the numerator of (1-2^(n-k+1))/(1-2^(k+1)).

1, 3, 1, 7, 1, 1, 15, 7, 3, 1, 31, 5, 1, 1, 1, 63, 31, 15, 7, 3, 1, 127, 21, 31, 1, 7, 1, 1, 255, 127, 9, 31, 15, 1, 3, 1, 511, 85, 127, 21, 1, 5, 7, 1, 1, 1023, 511, 255, 127, 63, 31, 15, 7, 3, 1, 2047, 341, 73, 17, 127, 1, 31, 1, 1, 1, 1, 4095, 2047, 1023

Offset

0,2

Comments

The denominators are given in A228035.

The first column is A000225, the second column is A213243, and the third column is A213245.

Links

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000225, A213243, A213245, A228035.

Sequence in context: A097862 A097612 A136011 * A021991 A112132 A053381

Adjacent sequences: A227981 A227982 A227983 * A227985 A227986 A227987

Keyword

nonn,tabl,frac

Author

Vincenzo Librandi, Aug 12 2013

Status

approved