A162594 Differences of cubes: T(n,n) = n^3, T(n,k) = T(n,k+1) - T(n-1,k), 0 <= k < n, triangle read by rows.

0, 1, 1, 6, 7, 8, 6, 12, 19, 27, 0, 6, 18, 37, 64, 0, 0, 6, 24, 61, 125, 0, 0, 0, 6, 30, 91, 216, 0, 0, 0, 0, 6, 36, 127, 343, 0, 0, 0, 0, 0, 6, 42, 169, 512, 0, 0, 0, 0, 0, 0, 6, 48, 217, 729, 0, 0, 0, 0, 0, 0, 0, 6, 54, 271, 1000, 0, 0, 0, 0, 0, 0, 0, 0, 6, 60, 331, 1331

Offset: 0

Author

Reinhard Zumkeller, Jul 07 2009

Keywords

• nonn
• tabl

Comments

T(n,n) = A000578(n);

T(n,n-1) = A003215(n-1), n > 0;

T(n,n-2) = A008588(n-2), n > 1;

T(n,n-3) = A010722(n-3), n > 2;

T(n,n-j) = A000004(n-j), 4 <= j <= n;

for n > 2: sum of n-th row = (n+1)^3.

Examples

			Triangle begins:
  0,
  1,  1,
  6,  7,  8,
  6, 12, 19, 27,
  0,  6, 18, 37, 64,
  0,  0,  6, 24, 61, 125,
  ...
		

Links

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

Crossrefs

Cf. A162593 (differences of squares).

Programs

Mathematica

T[n_, n_] := n^3; 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 *)

PARI

T(n, k) = if (k==n, n^3, T(n, k+1) - T(n-1, k));
tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print); \\ Michel Marcus, Jul 05 2018