A237444 Triangle read by rows, T(n,k) is difference of column sum and row sum of natural numbers filled in n x n square.
0, 1, -1, 6, 0, -6, 18, 6, -6, -18, 40, 20, 0, -20, -40, 75, 45, 15, -15, -45, -75, 126, 84, 42, 0, -42, -84, -126, 196, 140, 84, 28, -28, -84, -140, -196, 288, 216, 144, 72, 0, -72, -144, -216, -288, 405, 315, 225, 135, 45, -45, -135, -225, -315, -405, 550, 440, 330, 220, 110, 0, -110, -220, -330, -440, -550, 726, 594, 462, 330, 198, 66, -66
Offset: 1
Examples
Triangle begins: n/k 1 2 3 4 5 6 7 8 9 ... 1 0 2 1 -1 3 6 0 -6 4 18 6 -6 18 5 40 20 0 -20 -40 6 75 45 15 -15 -45 -75 7 126 84 42 0 -42 -84 -126 8 196 140 84 28 -28 -84 -140 -196 9 288 216 144 72 0 -72 -144 -216 -288 ... ... A082375 begins: 0; 1; 2, 0; 3, 1; 4, 2, 0; 5, 3, 1; 6, 4, 2, 0; 7, 5, 3, 1; 8, 6, 4, 2, 0; 9, 7, 5, 3, 1; ..... A000217 (triangular numbers) begins: 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ... A082375(n,k)*A000217(n) begins: 0; 1; 6, 0; 18, 6; 40, 20, 0; 75, 45, 15; 126, 84, 42, 0; 196, 140, 84, 28; 288, 216, 144, 72, 0; 405, 315, 225, 135, 45; ... - _Philippe Deléham_, Feb 08 2014
Links
- Kival Ngaokrajang, Illustration for n = 1..5
Formula
T(n,k) = - T(n,n-k+1), T(2n+1,n+1)= 0. - Philippe Deléham, Feb 08 2014
Comments