A251630 Column sums of the n X n square array filled with numbers from 1 to n^2, row by row, from left to right.

1, 4, 6, 12, 15, 18, 28, 32, 36, 40, 55, 60, 65, 70, 75, 96, 102, 108, 114, 120, 126, 154, 161, 168, 175, 182, 189, 196, 232, 240, 248, 256, 264, 272, 280, 288, 333, 342, 351, 360, 369, 378, 387, 396, 405, 460, 470, 480, 490, 500, 510, 520, 530

Offset: 1

Author

Wolfdieter Lang, Dec 09 2014

Keywords

• nonn
• easy
• tabl

Comments

This triangle has been considered by Kival Ngaokrajang as a companion of A241016. See the link given there, the second triangle.

Examples

			The n=4 square array is:
1   2  3  4
5   6  7  8
9  10 11 12
13 14 15 16
and the column sums are 28 32 36 40, which appear
in row n=4 of the triangle T.
The triangle T(n,k) begins:
n\k   1   2   3   4   5   6   7   8   9  10 ...
1:    1
2:    4   6
3:   12  15  18
4:   28  32  36  40
5:   55  60  65  70  75
6:   96 102 108 114 120 126
7:  154 161 168 175 182 189 196
8:  232 240 248 256 264 272 280 288
9:  333 342 351 360 369 378 387 396 405
10: 460 470 480 490 500 510 520 530 540 550
...
		

Crossrefs

Cf. A002411 (main diagonal), A006000 (column k=1), A241016.

Formula

T(n, k) = sum(n*(j-1)+ k, j=1..n), n >= k >= 1.

T(n, k) = n*(binomial(n+1, 2) + (k-n)).