A162594 - OEIS

%I #9 Jul 05 2018 07:22:08

%S 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,

%T 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,

%U 729,0,0,0,0,0,0,0,6,54,271,1000,0,0,0,0,0,0,0,0,6,60,331,1331

%N 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.

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

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

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

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

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

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

%H G. C. Greubel, <a href="/A162594/b162594.txt">Rows n = 0..99 of triangle, flattened</a>

%e Triangle begins:

%e   0,

%e   1,  1,

%e   6,  7,  8,

%e   6, 12, 19, 27,

%e   0,  6, 18, 37, 64,

%e   0,  0,  6, 24, 61, 125,

%e   ...

%t 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 *)

%o (PARI) T(n, k) = if (k==n, n^3, T(n, k+1) - T(n-1, k));

%o tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Jul 05 2018

%Y Cf. A162593 (differences of squares).

%K nonn,tabl

%O 0,4

%A _Reinhard Zumkeller_, Jul 07 2009