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

Author

T. D. Noe, Jan 21 2011

Keywords

• nonn
• hard
• tabf

Comments

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

Examples

			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
		

References

• See A180442.

Links

• 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)

Crossrefs

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