A211516 - OEIS

%I #7 Nov 28 2021 13:40:55

%S 0,0,1,3,3,5,7,9,12,14,16,18,20,24,28,32,34,36,39,43,47,51,55,59,63,

%T 67,71,75,79,83,87,91,96,102,108,114,118,122,126,130,134,140,146,152,

%U 158,164,170,176,182,186,191,197,203,209,215,221,227,233,239,245

%N Number of ordered triples (w,x,y) with all terms in {1,...,n} and w^2=x+y.

%C For a guide to related sequences, see A211422.

%F Conjecture: a(n) = -(2*n + 5/3)*w(n) + w(n)^2 + (2/3)*w(n)^3 + (2*n + 5/6)*w(2*n) - (1/2)*w(2*n)^2 - (1/3)*w(2*n)^3, where w = A000196. - _Velin Yanev_, Nov 16 2021

%t t[n_] := t[n] = Flatten[Table[w^2 - x - y, {w, 1, n}, {x, 1, n}, {y, 1, n}]]

%t c[n_] := Count[t[n], 0]

%t t = Table[c[n], {n, 0, 70}]  (* A211516 *)

%Y Cf. A211422.

%K nonn

%O 0,4

%A _Clark Kimberling_, Apr 14 2012