OFFSET
1,2
COMMENTS
T(n,1) = n, T(n,n) = A000217(n) = 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:
1
2, 3
3, 4, 6
4, 5, 7,10
5, 6, 9,11,15
6, 7,10,13,16,21
7, 8,12,16,19,22,28
8, 9,13,17,21,25,29,36
9,10,15,19,25,28,33,37,45
10,11,16,22,26,31,37,41,46, 55
11,12,18,23,29,36,40,45,51, 56, 66
12,13,19,25,31,37,43,49,55, 61, 67, 78
13,14,21,28,35,40,49,53,61, 67, 73, 79, 91
14,15,22,29,36,43,50,57,64, 71, 78, 85, 92,105
15,16,24,31,39,46,54,64,69, 76, 84, 91, 99,106,120
16,17,25,34,41,51,58,65,73, 82, 91, 97,106,113,121,136
17,18,27,35,45,52,61,69,81, 86, 95,103,113,120,129,137,153
18,19,28,37,46,55,64,73,82, 91,100,109,118,127,136,145,154,171
19,20,30,40,49,58,70,77,87,100,106,115,127,134,144,154,163,172,190
20,21,31,41,51,61,71,81,91,101,111,121,131,141,151,161,171,181,191,210
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