A184763 Irregular triangle in which row n has the values of k>n such that Sum_{i=n..k} i^2 is a square.

24, 4, 580, 963, 29, 39, 56, 190, 2215, 32, 552057, 22908, 108, 111, 326, 39, 5345, 28, 21, 43, 308, 1221044, 116, 80, 6910, 48, 50, 73, 578, 624, 3625, 21624, 59, 364, 77, 123, 198, 609, 4087, 61281, 148856, 48, 96, 349, 686, 11918, 67, 93, 171, 15674, 147, 389, 3533, 2132, 92, 3238, 305, 282, 928, 116, 8516, 194, 22873, 36554, 99, 276, 26003, 136, 332

Offset

1,1

Comments

Sequence A184762 gives the length of row n. A180442 lists the nonempty rows.

References

See A180442.

Links

Table of n, a(n) for n=1..69.

Jon E. Schoenfield, List of all integer solutions (i.e., triples (n, k, m) where k > n and Sum_{i=n..k} i^2 = m^2) for n in 1..460 (includes a derivation of the elliptic curves and Magma code used to find the solutions)

Example

The triangle is
(row 1)  24
(row 3)  4, 580, 963
(row 7)  29, 39, 56, 190, 2215
(row 9)  32, 552057
(row 11) 22908
(row 13) 108
(row 15) 111, 326

Crossrefs

Cf. A184885 (number of squares in each sum), A184886 (sqrt of sums).

Sequence in context: A040562 A267285 A040563 * A107674 A040560 A040558

Adjacent sequences: A184760 A184761 A184762 * A184764 A184765 A184766

Keyword

nonn,hard,tabf

Author

T. D. Noe, Jan 21 2011

Status

approved