A214859 Triangle read by rows, T(n,k) = n^2 - k*(k+1)/2 if k*(k+1)/2 <= n^2.

0, 1, 0, 4, 3, 1, 9, 8, 6, 3, 16, 15, 13, 10, 6, 1, 25, 24, 22, 19, 15, 10, 4, 36, 35, 33, 30, 26, 21, 15, 8, 0, 49, 48, 46, 43, 39, 34, 28, 21, 13, 4, 64, 63, 61, 58, 54, 49, 43, 36, 28, 19, 9, 81, 80, 78, 75, 71, 66, 60, 53, 45, 36, 26, 15, 3, 100, 99, 97

Offset

0,4

Comments

Row lengths are in A214857.

Links

Alois P. Heinz, Rows n = 0..200, flattened

Formula

T(2*n,n) = A022264(n).

T(n,n) = n*(n-1)/2 = A000217(n-1).

Example

Triangle begins:
    0;
    1,   0;
    4,   3,   1;
    9,   8,   6,   3;
   16,  15,  13,  10,   6,   1;
   25,  24,  22,  19,  15,  10,   4;
   36,  35,  33,  30,  26,  21,  15,  8,  0;
   49,  48,  46,  43,  39,  34,  28, 21, 13,  4;
   64,  63,  61,  58,  54,  49,  43, 36, 28, 19,  9;
   81,  80,  78,  75,  71,  66,  60, 53, 45, 36, 26, 15,  3;
  100,  99,  97,  94,  90,  85,  79, 72, 64, 55, 45, 34, 22,  9;
  121, 120, 118, 115, 111, 106, 100, 93, 85, 76, 66, 55, 43, 30, 16, 1;
  ...

Mathematica

Table[s = {}; k = 0; While[tri = k*(k + 1)/2; tri <= n^2, AppendTo[s, n^2 - tri]; k++]; s, {n, 0, 10}] (* T. D. Noe, Mar 11 2013 *)

Crossrefs

Cf. Diagonals: A000217, A034856, A055999,

Columns: A000290, A005563, A028872, A028878.

Sequence in context: A165732 A197698 A193011 * A123160 A109692 A039758

Adjacent sequences: A214856 A214857 A214858 * A214860 A214861 A214862

Keyword

nonn,easy,tabf

Author

Philippe Deléham, Mar 09 2013

Status

approved