A192655 Floor-Sqrt transform of central binomial coefficients (A000984).

1, 1, 2, 4, 8, 15, 30, 58, 113, 220, 429, 839, 1644, 3224, 6333, 12454, 24516, 48307, 95263, 188003, 371276, 733660, 1450551, 2869395, 5678697, 11243247, 22269228, 44124136, 87456792, 173399153, 343896178, 682223096, 1353744488, 2686899408, 5334139244, 10591802387

Offset: 0

Author

Emanuele Munarini, Jul 07 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000196, A000984.

Programs

Magma

[Floor(Sqrt(Binomial(2*n,n))): n in [0..40]]; // Vincenzo Librandi, Apr 01 2012

Mathematica

Table[Floor[Sqrt[Binomial[2n,n]]],{n,0,100}]

Maxima

makelist(floor(sqrt(binomial(2*n,n))),n,0,24);

PARI

a(n) = sqrtint(binomial(2*n,n)) \\ Jason Yuen, Oct 21 2024

Formula

a(n) = floor(sqrt(binomial(2*n,n))).

a(n) = A000196(A000984(n)). - Jason Yuen, Oct 21 2024