A279417 Triangle read by rows: T(n,k), n >= k >= 1, is the number of grid points on or below the diagonal of an n X k grid.

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

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

Cf. A279416.

Sequence in context: A317838 A213938 A031501 * A203996 A059442 A225273

Adjacent sequences: A279414 A279415 A279416 * A279418 A279419 A279420

Keyword

nonn,tabl,easy

Author

Lars Blomberg, Feb 22 2017

Status

approved