cp's OEIS Frontend

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.

%I A251630 #11 Dec 09 2014 08:13:13
%S A251630 1,4,6,12,15,18,28,32,36,40,55,60,65,70,75,96,102,108,114,120,126,154,
%T A251630 161,168,175,182,189,196,232,240,248,256,264,272,280,288,333,342,351,
%U A251630 360,369,378,387,396,405,460,470,480,490,500,510,520,530
%N 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.
%C A251630 This triangle has been considered by _Kival Ngaokrajang_ as a companion of A241016. See the link given there, the second triangle.
%F A251630 T(n, k) = sum(n*(j-1)+ k, j=1..n), n >= k >= 1.
%F A251630 T(n, k) = n*(binomial(n+1, 2) + (k-n)).
%e A251630 The n=4 square array is:
%e A251630 1   2  3  4
%e A251630 5   6  7  8
%e A251630 9  10 11 12
%e A251630 13 14 15 16
%e A251630 and the column sums are 28 32 36 40, which appear
%e A251630 in row n=4 of the triangle T.
%e A251630 The triangle T(n,k) begins:
%e A251630 n\k   1   2   3   4   5   6   7   8   9  10 ...
%e A251630 1:    1
%e A251630 2:    4   6
%e A251630 3:   12  15  18
%e A251630 4:   28  32  36  40
%e A251630 5:   55  60  65  70  75
%e A251630 6:   96 102 108 114 120 126
%e A251630 7:  154 161 168 175 182 189 196
%e A251630 8:  232 240 248 256 264 272 280 288
%e A251630 9:  333 342 351 360 369 378 387 396 405
%e A251630 10: 460 470 480 490 500 510 520 530 540 550
%e A251630 ...
%Y A251630 Cf. A002411 (main diagonal), A006000 (column k=1), A241016.
%K A251630 nonn,easy,tabl
%O A251630 1,2
%A A251630 _Wolfdieter Lang_, Dec 09 2014