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Irregular triangle in which row n has the values of k>n such that Sum_{i=n..k} i^2 is a square.
9

%I #15 Jul 06 2019 15:30:23

%S 24,4,580,963,29,39,56,190,2215,32,552057,22908,108,111,326,39,5345,

%T 28,21,43,308,1221044,116,80,6910,48,50,73,578,624,3625,21624,59,364,

%U 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

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

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

%D See A180442.

%H Jon E. Schoenfield, <a href="/A184763/a184763.txt">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)</a>

%e The triangle is

%e (row 1) 24

%e (row 3) 4, 580, 963

%e (row 7) 29, 39, 56, 190, 2215

%e (row 9) 32, 552057

%e (row 11) 22908

%e (row 13) 108

%e (row 15) 111, 326

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

%K nonn,hard,tabf

%O 1,1

%A _T. D. Noe_, Jan 21 2011