A162593 - OEIS

%I #10 Jul 05 2018 04:59:29

%S 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,

%T 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,

%U 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

%N 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.

%C T(n,n) = A000290(n);

%C T(n,n-1) = A005408(n-1), n > 0;

%C T(n,n-2) = A007395(n-2), n > 1;

%C T(n,n-j) = A000004(n-j), 3 <= j <= n;

%C sum of n-th row = if n <= 1 then 2*n else (n+1)^2.

%H G. C. Greubel, <a href="/A162593/b162593.txt">Rows n=0..99 of triangle, flattened</a>

%e From _Jon E. Schoenfield_, Jul 04 2018: (Start)

%e Table begins

%e .

%e   n\k| 0   1   2   3   4   5   6   7   8   9  10  11  12

%e   ---+--------------------------------------------------

%e    0 | 0

%e    1 | 1   1

%e    2 | 2   3   4

%e    3 | 0   2   5   9

%e    4 | 0   0   2   7  16

%e    5 | 0   0   0   2   9  25

%e    6 | 0   0   0   0   2  11  36

%e    7 | 0   0   0   0   0   2  13  49

%e    8 | 0   0   0   0   0   0   2  15  64

%e    9 | 0   0   0   0   0   0   0   2  17  81

%e   10 | 0   0   0   0   0   0   0   0   2  19 100

%e   11 | 0   0   0   0   0   0   0   0   0   2  21 121

%e   12 | 0   0   0   0   0   0   0   0   0   0   2  23 144

%e   ...

%e (End)

%t 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 *)

%Y Cf. A162594 (differences of cubes).

%K nonn,tabl

%O 0,4

%A _Reinhard Zumkeller_, Jul 07 2009