%I #10 Jul 05 2018 04:59:29
%S 0,1,1,2,3,4,0,2,5,9,0,0,2,7,16,0,0,0,2,9,25,0,0,0,0,2,11,36,0,0,0,0,
%T 0,2,13,49,0,0,0,0,0,0,2,15,64,0,0,0,0,0,0,0,2,17,81,0,0,0,0,0,0,0,0,
%U 2,19,100,0,0,0,0,0,0,0,0,0,2,21,121,0,0,0,0,0,0,0,0,0,0,2,23,144
%N Differences of squares: T(n,n) = n^2, T(n,k) = T(n,k+1) - T(n-1,k), 0 <= k < n, triangle read by rows.
%C T(n,n) = A000290(n);
%C T(n,n-1) = A005408(n-1), n > 0;
%C T(n,n-2) = A007395(n-2), n > 1;
%C T(n,n-j) = A000004(n-j), 3 <= j <= n;
%C sum of n-th row = if n <= 1 then 2*n else (n+1)^2.
%H G. C. Greubel, <a href="/A162593/b162593.txt">Rows n=0..99 of triangle, flattened</a>
%e From _Jon E. Schoenfield_, Jul 04 2018: (Start)
%e Table begins
%e .
%e n\k| 0 1 2 3 4 5 6 7 8 9 10 11 12
%e ---+--------------------------------------------------
%e 0 | 0
%e 1 | 1 1
%e 2 | 2 3 4
%e 3 | 0 2 5 9
%e 4 | 0 0 2 7 16
%e 5 | 0 0 0 2 9 25
%e 6 | 0 0 0 0 2 11 36
%e 7 | 0 0 0 0 0 2 13 49
%e 8 | 0 0 0 0 0 0 2 15 64
%e 9 | 0 0 0 0 0 0 0 2 17 81
%e 10 | 0 0 0 0 0 0 0 0 2 19 100
%e 11 | 0 0 0 0 0 0 0 0 0 2 21 121
%e 12 | 0 0 0 0 0 0 0 0 0 0 2 23 144
%e ...
%e (End)
%t T[n_, n_] := n^2; T[n_, k_] := T[n, k] = T[n, k + 1] - T[n - 1, k]; Table[T[n, k], {n, 0, 15}, {k, 0, n}] // Flatten (* _G. C. Greubel_, Jul 04 2018 *)
%Y Cf. A162594 (differences of cubes).
%K nonn,tabl
%O 0,4
%A _Reinhard Zumkeller_, Jul 07 2009