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A162593 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.

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