A278712 Triangle T read by rows: T(n, m), for n >= 2, and m = 1, 2, ..., n-1, equals the square root of the positive integer solution y of y^2 = x^3 - A(n, m)^2*x with the area A(n, m) = A249869(n, m) of the primitive Pythagorean triangle characterized by (n, m) or 0 if no such triangle exists.

6, 0, 15, 60, 0, 28, 0, 105, 0, 45, 210, 0, 0, 0, 66, 0, 315, 0, 231, 0, 91, 504, 0, 440, 0, 312, 0, 120, 0, 693, 0, 585, 0, 0, 0, 153, 990, 0, 910, 0, 0, 0, 510, 0, 190, 0, 1287, 0, 1155, 0, 935, 0, 627, 0, 231, 1716, 0, 0, 0, 1428, 0, 1140, 0, 0, 0, 276, 0, 2145, 0, 1989, 0, 1729, 0, 1365, 0, 897, 0, 325, 2730, 0, 2618, 0, 2394, 0, 0, 0, 1610, 0, 1050, 0, 378, 0, 3315, 0, 3135, 0, 0, 0, 2415, 0, 0, 0, 0, 0, 435

Offset

2,1

Comments

The corresponding solutions x are given in A278711, where also details are found.

Links

Table of n, a(n) for n=2..106.

Formula

T(n, m) = (n^2 - m^2)*n if n > m >= 1, gcd(n, m) = 1 and n+m is odd, and T(n, m) = 0 otherwise.

Example

The triangle T(n, m) begins:
n\m   1    2   3    4   5   6   7   8   9  10
2:    6
3:    0   15
4:   60    0  28
5:    0  105   0   45
6:  210    0   0    0  66
7:    0  315   0  231   0  91
8:  504    0 440    0 312   0 120
9:    0  693   0  585   0   0   0 153
10: 990    0 910    0   0   0 510   0 190
11:   0 1287   0 1155   0 935   0 627   0 231
...
n = 12: 1716 0 0 0 1428 0 1140 0 0 0 276,
n = 13: 0 2145 0 1989 0 1729 0 1365 0 897 0 325,
n = 14: 2730 0 2618 0 2394 0 0 0 1610 0 1050 0 378,
n = 15: 0 3315 0 3135 0 0 0 2415 0 0 0 0 0 435.
...
For the solutions [x,y] see A278711.

Crossrefs

Cf. A278711.

Sequence in context: A069828 A340951 A270536 * A057401 A308236 A019134

Adjacent sequences: A278709 A278710 A278711 * A278713 A278714 A278715

Keyword

nonn,tabl,easy

Author

Wolfdieter Lang, Nov 27 2016

Status

approved