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.

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, 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, 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

Offset: 0

Author

Reinhard Zumkeller, Jul 07 2009

Keywords

• nonn
• tabl

Comments

T(n,n) = A000290(n);

T(n,n-1) = A005408(n-1), n > 0;

T(n,n-2) = A007395(n-2), n > 1;

T(n,n-j) = A000004(n-j), 3 <= j <= n;

sum of n-th row = if n <= 1 then 2*n else (n+1)^2.

Examples

			From _Jon E. Schoenfield_, Jul 04 2018: (Start)
Table begins
.
  n\k| 0   1   2   3   4   5   6   7   8   9  10  11  12
  ---+--------------------------------------------------
   0 | 0
   1 | 1   1
   2 | 2   3   4
   3 | 0   2   5   9
   4 | 0   0   2   7  16
   5 | 0   0   0   2   9  25
   6 | 0   0   0   0   2  11  36
   7 | 0   0   0   0   0   2  13  49
   8 | 0   0   0   0   0   0   2  15  64
   9 | 0   0   0   0   0   0   0   2  17  81
  10 | 0   0   0   0   0   0   0   0   2  19 100
  11 | 0   0   0   0   0   0   0   0   0   2  21 121
  12 | 0   0   0   0   0   0   0   0   0   0   2  23 144
  ...
(End)
		

Links

• G. C. Greubel, Rows n=0..99 of triangle, flattened

Crossrefs

Cf. A162594 (differences of cubes).

Programs

Mathematica

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 *)