OFFSET
1,5
COMMENTS
T(n,1) = 0, T(n,n) = A000217(n-1) = n*(n-1)/2.
LINKS
Lars Blomberg, Table of n, a(n) for n = 1..9870 (the first 140 rows)
FORMULA
T(n,k) = (k*n - (gcd(n-1, k-1) + 1)) / 2.
EXAMPLE
Triangle begins:
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, 7,11,15,19,23,27,28
0, 8,12,17,20,26,30,35,36
0, 9,14,18,24,29,33,39,44,45
0,10,15,21,26,30,37,43,48,54, 55
0,11,17,23,29,35,41,47,53,59, 65, 66
0,12,18,24,30,38,42,51,56,63, 70, 77, 78
0,13,20,27,34,41,48,55,62,69, 76, 83, 90, 91
0,14,21,29,36,44,51,56,66,74, 81, 89, 96,104,105
0,15,23,30,39,45,54,63,71,78, 85, 95,102,111,119,120
0,16,24,33,40,50,58,67,72,84, 92,101,108,118,126,135,136
0,17,26,35,44,53,62,71,80,89, 98,107,116,125,134,143,152,153
0,18,27,36,46,56,63,75,84,90,103,113,120,132,141,150,160,170,171
0,19,29,39,49,59,69,79,89,99,109,119,129,139,149,159,169,179,189,190
MATHEMATICA
Table[(k n - (GCD[n - 1, k - 1] + 1))/2, {n, 12}, {k, n}] // Flatten (* Michael De Vlieger, Feb 22 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Lars Blomberg, Feb 22 2017
STATUS
approved