login
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.
2
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
0,4
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.
EXAMPLE
Triangle begins:
0,
1, 1,
6, 7, 8,
6, 12, 19, 27,
0, 6, 18, 37, 64,
0, 0, 6, 24, 61, 125,
...
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 *)
PROG
(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
CROSSREFS
Cf. A162593 (differences of squares).
Sequence in context: A085661 A265276 A286474 * A229948 A198124 A120207
KEYWORD
nonn,tabl
AUTHOR
Reinhard Zumkeller, Jul 07 2009
STATUS
approved