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

0,4

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.

Links

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

Example

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)

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 *)

Crossrefs

Cf. A162594 (differences of cubes).

Sequence in context: A230431 A190886 A257845 * A279125 A011025 A286248

Adjacent sequences: A162590 A162591 A162592 * A162594 A162595 A162596

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jul 07 2009

Status

approved