A256000 Numbers whose square can be written as sum of at least 3 consecutive triangular numbers in two ways.

286, 826, 2739, 3971, 5698, 9196, 10166, 10697, 22990, 61006, 132795, 416790, 766480, 809380, 2396870, 2904434, 3459006, 3688802, 4518514, 11725659, 13111098, 13998608, 15709122, 22173027, 22365267, 23636272, 23823988, 32186742, 33630662, 33658710, 39502086, 46387924, 59101625, 62381858, 89841192

Offset

1,1

Comments

Apparently there is an infinity of such numbers and there are no cases of 3 ways.

Links

Table of n, a(n) for n=1..35.

Example

4518514^2 = T(18801)+..+T(50546) = T(52361)+..+T(64316), where T(n) = A000217(n).

Crossrefs

Cf. A000217 (triangular numbers), A257274.

Sequence in context: A090089 A204379 A025384 * A253329 A356422 A329392

Adjacent sequences: A255997 A255998 A255999 * A256001 A256002 A256003

Keyword

nonn,changed

Author

Zak Seidov, May 06 2015

Extensions

a(10), a(20)-a(35) from Chai Wah Wu, Jan 21 2016

Status

approved