A178067 Triangle read by rows: T(n,k) = (n^2 + k)*(n - k + 1)/2.

1, 5, 3, 15, 11, 6, 34, 27, 19, 10, 65, 54, 42, 29, 15, 111, 95, 78, 60, 41, 21, 175, 153, 130, 106, 81, 55, 28, 260, 231, 201, 170, 138, 105, 71, 36, 369, 332, 294, 255, 215, 174, 132, 89, 45, 505, 459, 412, 364, 315, 265, 214, 162, 109, 55, 671, 615, 558, 500, 441, 381, 320, 258, 195, 131, 66

Offset: 1

Author

Gary W. Adamson, May 18 2010

Keywords

• nonn
• tabl
• easy

Examples

			First few rows of the triangle:
    1;
    5,   3;
   15,  11,   6;
   34,  27,  19,  10;
   65,  54,  42,  29,  15;
  111,  95,  78,  60,  41,  21;
  175, 153, 130, 106,  81,  55,  28;
  260, 231, 201, 170, 138, 105,  71,  36;
  369, 332, 294, 255, 215, 174, 132,  89,  45;
  505, 459, 412, 364, 315, 265, 214, 162, 109,  55;
  671, 615, 558, 500, 441, 381, 320, 258, 195, 131, 66;
  ...
Example: Row 3 = (15, 11 6) since row 3 of A000027 as a triangle = (4, 5, 6); then taking partial sums from the right.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)

Crossrefs

Column 1 is A006003.

Row sums are A132117.

Main diagonal is A000217.

Formula

As infinite lower triangular matrices, A000027 * A000012 (the all 1's triangle).

Extensions

Name changed and terms a(37) and beyond from Andrew Howroyd, Apr 17 2021