login
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
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
1,2
COMMENTS
This triangle has been considered by Kival Ngaokrajang as a companion of A241016. See the link given there, the second triangle.
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)).
EXAMPLE
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.
Sequence in context: A058219 A131863 A074870 * A256241 A364385 A247632
KEYWORD
nonn,easy,tabl
AUTHOR
Wolfdieter Lang, Dec 09 2014
STATUS
approved