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Irregular triangle read by rows: the n-th row gives the x-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 08:30:44

%S 2,2,2,2,3,2,2,3,2,2,3,4,2,2,3,2,4,2,3,2,5,2,3,4,2,2,3,2,4,5,2,3,2,6,

%T 2,3,4,2,5,2,3,2,4,2,3,6,2,5,2,3,4,7,2,2,3,2,4,5,6,2,3,2,2,3,4,7,2,5,

%U 2,3,6,8,2,4,2,3,2,5,2,3,4,7,2,6,2,3,2,4,5,8

%N Irregular triangle read by rows: the n-th row gives the x-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 column indices corresponding to n in the triangle A351153.

%e Triangle begins:

%e 2;

%e 2;

%e 2;

%e 2, 3;

%e 2;

%e 2, 3;

%e 2;

%e 2, 3, 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,d+1]]];r,{n,3,43}]//Flatten

%Y Cf. A341829, A351153, A136107 (row length or solutions number), A351285 (y-values).

%K nonn,tabf

%O 3,1

%A _Stefano Spezia_, Feb 06 2022