A few years ago I mentioned an effective way to list the square triangular numbers by brute force finding the first few, and then computing each new one from the previous six so as to annihilate the determinant of a 4x4 Toeplitz matrix. How can this fail: (c256) subset(-9..9,lambda([x],integerp(sqrt(binomial(x+1,2))))) (d256) [- 9, - 2, - 1, 0, 1, 8] (c257) genmatrix(lambda([i,j],(''(endcons(x,%*(%+1)/2)))[i+j-1]),4) [ 36 1 0 0 ] [ ] [ 1 0 0 1 ] (d257) [ ] [ 0 0 1 36 ] [ ] [ 0 1 36 x ] (c258) sqrt(solve(det(%))) (d258) [sqrt(x) = 6 sqrt(35)] while this succeeds? (c261) delete(-1,subset(-50..9,lambda([x],integerp(sqrt(binomial(x+1,2)))))) (d261) [- 50, - 9, - 2, 0, 1, 8] (c262) genmatrix(lambda([i,j],(''(endcons(x,%*(%+1)/2)))[i+j-1]),4) [ 1225 36 1 0 ] [ ] [ 36 1 0 1 ] (d262) [ ] [ 1 0 1 36 ] [ ] [ 0 1 36 x ] (c263) sqrt(solve(det(%))) (d263) [sqrt(x) = 35] (c280) genmatrix(lambda([i,j],(''(append(d261*(d261+1)/2,[35^2,x])))[i+j]),4) [ 36 1 0 1 ] [ ] [ 1 0 1 36 ] (d280) [ ] [ 0 1 36 1225 ] [ ] [ 1 36 1225 x ] (c281) sqrt(solve(det(%))) (d281) [sqrt(x) = 204] etc. --rwg