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A228035
Triangle T(n,k), read by rows: T(n,k) is the denominator of (1-2^(n-k+1))/(1-2^(k+1)).
2
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
KEYWORD
nonn,tabl,frac
AUTHOR
Vincenzo Librandi, Aug 12 2013
STATUS
approved