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A214859
Triangle read by rows, T(n,k) = n^2 - k*(k+1)/2 if k*(k+1)/2 <= n^2.
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
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,
Sequence in context: A165732 A197698 A193011 * A123160 A109692 A039758
KEYWORD
nonn,easy,tabf
AUTHOR
Philippe Deléham, Mar 09 2013
STATUS
approved