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Triangle read by rows: a(n, k) is the numerator of (n + (n-1) + ... + (n-k+1))/(1 + 2 + ... + k), 0 < k <= n.
8

%I #10 Oct 21 2019 02:12:08

%S 1,2,1,3,5,1,4,7,3,1,5,3,2,7,1,6,11,5,9,4,1,7,13,3,11,5,9,1,8,5,7,13,

%T 2,11,5,1,9,17,4,3,7,13,3,11,1,10,19,9,17,8,15,7,13,6,1,11,7,5,19,3,

%U 17,2,5,7,13,1,12,23,11,21,10,19,9,17,8,15,7,1,13,25,6,23,11,3,5,19,9,17,4

%N Triangle read by rows: a(n, k) is the numerator of (n + (n-1) + ... + (n-k+1))/(1 + 2 + ... + k), 0 < k <= n.

%C A093415 gives the corresponding denominators.

%F a(n, k) = (2n+1-k)/gcd(2n+1-k, k+1).

%e Triangle a(n,k) (with rows n >= 1 and columns k >= 1) begins as follows:

%e 1;

%e 2, 1;

%e 3, 5, 1;

%e 4, 7, 3, 1;

%e 5, 3, 2, 7, 1;

%e 6, 11, 5, 9, 4, 1;

%e 7, 13, 3, 11, 5, 9, 1;

%e 8, 5, 7, 13, 2, 11, 5, 1;

%e 9, 17, 4, 3, 7, 13, 3, 11, 1;

%e ... - _Petros Hadjicostas_, Oct 20 2019

%Y Cf. A093413, A093414, A093415.

%K easy,nonn,tabl,frac

%O 1,2

%A _Amarnath Murthy_, Mar 30 2004

%E Edited and extended by _David Wasserman_, Feb 01 2006