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A232765 Values of y solving x^2 = floor(y^2/3 + y). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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.

LINKS

Table of n, a(n) for n=1..33.

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

PROG

(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

CROSSREFS

Cf. A005320, A011943, A001570, A110293.

Sequence in context: A071258 A120333 A000368 * A094255 A192234 A069563

Adjacent sequences:  A232762 A232763 A232764 * A232766 A232767 A232768

KEYWORD

nonn

AUTHOR

Richard R. Forberg, Nov 29 2013

EXTENSIONS

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

STATUS

approved

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Last modified April 23 07:51 EDT 2019. Contains 322381 sequences. (Running on oeis4.)