A234369 Floor(AGM(1, triangular(n))), where AGM denotes the arithmetic-geometric mean.

0, 1, 1, 2, 4, 5, 7, 9, 11, 13, 16, 18, 21, 24, 27, 30, 33, 37, 41, 44, 48, 53, 57, 61, 66, 71, 76, 81, 86, 91, 97, 102, 108, 114, 120, 126, 132, 139, 145, 152, 159, 166, 173, 180, 187, 195, 202, 210, 218, 226, 234, 242, 251, 259, 268, 277, 286, 295, 304, 313, 323, 332

Offset: 0

Author

Alex Ratushnyak, Dec 25 2013

Keywords

• nonn

Crossrefs

Cf. A000217, A127758, A234363, A234368.

Programs

Mathematica

Table[Floor[ArithmeticGeometricMean[1, n*(n+1)/2]], {n, 0, 100}] (* Vaclav Kotesovec, May 09 2016 *)
Floor[ArithmeticGeometricMean[1,#]]&/@Accumulate[Range[0,100]] (* Harvey P. Dale, Nov 01 2022 *)

Formula

a(n) ~ Pi*n^2/(8*log(n) + 4*log(2)). - Vaclav Kotesovec, May 09 2016