A162594 -id:A162594 - cp's OEIS frontend

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

Reinhard Zumkeller, Jul 07 2009

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.

			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)

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

Cf. A162594 (differences of cubes).

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 *)

cp's OEIS Frontend

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.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica