A232765 Values of y solving x^2 = floor(y^2/3 + y).

0, 1, 4, 9, 28, 73, 144, 409, 1036, 2025, 5716, 14449, 28224, 79633, 201268, 393129, 1109164, 2803321, 5475600, 15448681, 39045244, 76265289, 215172388, 543830113, 1062238464, 2996964769, 7574576356, 14795073225, 41742334396, 105500238889, 206068786704, 581395716793, 1469428768108

Offset: 1

Author

Richard R. Forberg, Nov 29 2013

Keywords

• nonn

Comments

The corresponding values of x are given by A232771.

a(n) + 3 gives the values of y solving x^2 = floor(y^2/3 - y), and yields the same values for x.

a(3n+1) are squares whose square roots are given by A005320.

Let b(n) equal the second differences of a(n) where b(1) = 2. Then, for n>0, b(3n-1) = b(3n-2) = 2* A001570(n+1); b(3n)= 2*A011943(n); and b(3n) = (b(3n+1) + b(3n-1))/2.

Crossrefs

Cf. A005320, A011943, A001570, A110293.

Programs

PARI

is(n)=issquare(n^2\3+n)
print1("0, 1");for(x=3,99,y=round(sqrt(3)*x-3/2);if(is(y),print1(", "y))) \\ Charles R Greathouse IV, Dec 09 2013

Formula

Empirical g.f.: -x^2*(x+1)*(x^2+x+1)^2 / ((x-1)*(x^6-14*x^3+1)). - Colin Barker, Dec 30 2014

Extensions

a(23) corrected by Colin Barker, Dec 30 2014