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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.

%I A162594 #9 Jul 05 2018 07:22:08
%S A162594 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 A162594 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 A162594 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 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.
%C A162594 T(n,n) = A000578(n);
%C A162594 T(n,n-1) = A003215(n-1), n > 0;
%C A162594 T(n,n-2) = A008588(n-2), n > 1;
%C A162594 T(n,n-3) = A010722(n-3), n > 2;
%C A162594 T(n,n-j) = A000004(n-j), 4 <= j <= n;
%C A162594 for n > 2: sum of n-th row = (n+1)^3.
%H A162594 G. C. Greubel, <a href="/A162594/b162594.txt">Rows n = 0..99 of triangle, flattened</a>
%e A162594 Triangle begins:
%e A162594   0,
%e A162594   1,  1,
%e A162594   6,  7,  8,
%e A162594   6, 12, 19, 27,
%e A162594   0,  6, 18, 37, 64,
%e A162594   0,  0,  6, 24, 61, 125,
%e A162594   ...
%t A162594 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 A162594 (PARI) T(n, k) = if (k==n, n^3, T(n, k+1) - T(n-1, k));
%o A162594 tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, Jul 05 2018
%Y A162594 Cf. A162593 (differences of squares).
%K A162594 nonn,tabl
%O A162594 0,4
%A A162594 _Reinhard Zumkeller_, Jul 07 2009