

A214859


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


0



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
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OFFSET

0,4


COMMENTS

Row lengths are in A214857.


LINKS

Table of n, a(n) for n=0..68.


FORMULA

T(2*n,n) = A022264(n).
T(n,n) = n*(n1)/2 = A000217(n1).


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 A039758 A109692
Adjacent sequences: A214856 A214857 A214858 * A214860 A214861 A214862


KEYWORD

nonn,easy,tabf


AUTHOR

Philippe Deléham, Mar 09 2013


STATUS

approved



