login
Irregular triangle read by rows in which row n gives the y-values of the solutions of the equation 2*(x - 1)*y - (x - 3)*x = 2*n for 0 < x <= y.
2

%I #9 Feb 12 2022 08:30:12

%S 2,3,4,5,3,6,7,4,8,9,5,4,10,11,6,12,5,13,7,14,5,15,8,6,16,17,9,18,7,6,

%T 19,10,20,6,21,11,8,22,7,23,12,24,9,25,13,7,26,8,27,14,10,7,28,29,15,

%U 30,11,9,8,31,16,32,33,17,12,8,34,10,35,18,9,8,36,13

%N Irregular triangle read by rows in which row n gives the y-values of the solutions of the equation 2*(x - 1)*y - (x - 3)*x = 2*n for 0 < x <= y.

%C Equivalently, the n-th row gives the row indices corresponding to n in the triangle A351153.

%e Triangle begins:

%e 2;

%e 3;

%e 4;

%e 5, 3;

%e 6;

%e 7, 4;

%e 8;

%e 9, 5, 4;

%e ...

%t Table[r={};For[d=1,d<Floor[(Sqrt[1+8n]-1)/2],d++,If[Divisible[2n+(d-2)(d+1),2d],AppendTo[r,(2n+(d-2)(d+1))/(2d)]]];r,{n,3,37}]//Flatten

%Y Cf. A341830, A351153, A136107(row length or solutions number), A351284 (x-values).

%K nonn,tabf

%O 3,1

%A _Stefano Spezia_, Feb 06 2022