A279416 - OEIS

%I #10 Sep 11 2021 18:57:17

%S 0,0,1,0,2,3,0,3,5,6,0,4,6,9,10,0,5,8,11,14,15,0,6,9,12,16,20,21,0,7,

%T 11,15,19,23,27,28,0,8,12,17,20,26,30,35,36,0,9,14,18,24,29,33,39,44,

%U 45,0,10,15,21,26,30,37,43,48,54,55,0,11,17,23,29,35

%N Triangle read by rows: T(n,k), n >= k >= 1, is the number of grid points below the diagonal of an n X k grid.

%C T(n,1) = 0, T(n,n) = A000217(n-1) = n*(n-1)/2.

%H Lars Blomberg, <a href="/A279416/b279416.txt">Table of n, a(n) for n = 1..9870</a> (the first 140 rows)

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

%e Triangle begins:

%e   0

%e   0, 1

%e   0, 2, 3

%e   0, 3, 5, 6

%e   0, 4, 6, 9,10

%e   0, 5, 8,11,14,15

%e   0, 6, 9,12,16,20,21

%e   0, 7,11,15,19,23,27,28

%e   0, 8,12,17,20,26,30,35,36

%e   0, 9,14,18,24,29,33,39,44,45

%e   0,10,15,21,26,30,37,43,48,54, 55

%e   0,11,17,23,29,35,41,47,53,59, 65, 66

%e   0,12,18,24,30,38,42,51,56,63, 70, 77, 78

%e   0,13,20,27,34,41,48,55,62,69, 76, 83, 90, 91

%e   0,14,21,29,36,44,51,56,66,74, 81, 89, 96,104,105

%e   0,15,23,30,39,45,54,63,71,78, 85, 95,102,111,119,120

%e   0,16,24,33,40,50,58,67,72,84, 92,101,108,118,126,135,136

%e   0,17,26,35,44,53,62,71,80,89, 98,107,116,125,134,143,152,153

%e   0,18,27,36,46,56,63,75,84,90,103,113,120,132,141,150,160,170,171

%e   0,19,29,39,49,59,69,79,89,99,109,119,129,139,149,159,169,179,189,190

%t Table[(k n - (GCD[n - 1, k - 1] + 1))/2, {n, 12}, {k, n}] // Flatten (* _Michael De Vlieger_, Feb 22 2017 *)

%Y Cf A279417.

%K nonn,tabl,easy

%O 1,5

%A _Lars Blomberg_, Feb 22 2017