A343426 Triangular numbers T(i) that can be expressed as the sum of 2 positive triangular numbers, T(j)+T(k), and for which i+j+k is a triangular number, where T is A000217.

276, 741, 17766, 30876, 42778, 43071, 44850, 54946, 73920, 99681, 163306, 184528, 254541, 310866, 446040, 524800, 963966, 1006071, 1046181, 1160526, 1258491, 1873080, 1929630, 2793066, 3034416, 3108771, 3121251, 3454506, 3635556, 4305645, 4317391, 4435731, 4831386, 4859403

Offset: 1

Author

Michel Marcus, Apr 15 2021

Keywords

• nonn

Examples

			276 = T(23) = 105 + 171 = T(14) + T(18) and 23+14+18 = 55 = T(10), so 276 is a term.
		

Links

• K. R. S. Sastry, Problem 518, The College Mathematics Journal, p. 64, Vol. 25, No. 1, Jan., 1994; Solution, Pythagorean Triples of Triangular Numbers, p. 69, Vol. 26, No. 1, Jan., 1995.

Crossrefs

Cf. A000217. Subsequence of A089982.

Programs

PARI

lista(nn) = {for (n=1, nn, my(t = n*(n+1)/2, kk); for (k=1, n-1, if (ispolygonal(t - k*(k+1)/2, 3, &kk), if (ispolygonal(n+k+kk, 3), print1(t, ", "); break;););););}