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A162593 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. 2
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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

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

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

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

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

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

LINKS

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

EXAMPLE

From Jon E. Schoenfield, Jul 04 2018: (Start)

Table begins

.

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

  ---+--------------------------------------------------

   0 | 0

   1 | 1   1

   2 | 2   3   4

   3 | 0   2   5   9

   4 | 0   0   2   7  16

   5 | 0   0   0   2   9  25

   6 | 0   0   0   0   2  11  36

   7 | 0   0   0   0   0   2  13  49

   8 | 0   0   0   0   0   0   2  15  64

   9 | 0   0   0   0   0   0   0   2  17  81

  10 | 0   0   0   0   0   0   0   0   2  19 100

  11 | 0   0   0   0   0   0   0   0   0   2  21 121

  12 | 0   0   0   0   0   0   0   0   0   0   2  23 144

  ...

(End)

MATHEMATICA

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 *)

CROSSREFS

Cf. A162594 (differences of cubes).

Sequence in context: A230431 A190886 A257845 * A279125 A011025 A286248

Adjacent sequences:  A162590 A162591 A162592 * A162594 A162595 A162596

KEYWORD

nonn,tabl

AUTHOR

Reinhard Zumkeller, Jul 07 2009

STATUS

approved

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Last modified May 11 16:48 EDT 2021. Contains 343805 sequences. (Running on oeis4.)