A251630 - OEIS

%I #11 Dec 09 2014 08:13:13

%S 1,4,6,12,15,18,28,32,36,40,55,60,65,70,75,96,102,108,114,120,126,154,

%T 161,168,175,182,189,196,232,240,248,256,264,272,280,288,333,342,351,

%U 360,369,378,387,396,405,460,470,480,490,500,510,520,530

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

%C This triangle has been considered by _Kival Ngaokrajang_ as a companion of A241016. See the link given there, the second triangle.

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

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

%e The n=4 square array is:

%e 1   2  3  4

%e 5   6  7  8

%e 9  10 11 12

%e 13 14 15 16

%e and the column sums are 28 32 36 40, which appear

%e in row n=4 of the triangle T.

%e The triangle T(n,k) begins:

%e n\k   1   2   3   4   5   6   7   8   9  10 ...

%e 1:    1

%e 2:    4   6

%e 3:   12  15  18

%e 4:   28  32  36  40

%e 5:   55  60  65  70  75

%e 6:   96 102 108 114 120 126

%e 7:  154 161 168 175 182 189 196

%e 8:  232 240 248 256 264 272 280 288

%e 9:  333 342 351 360 369 378 387 396 405

%e 10: 460 470 480 490 500 510 520 530 540 550

%e ...

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

%K nonn,easy,tabl

%O 1,2

%A _Wolfdieter Lang_, Dec 09 2014