A114459 Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2)+sqrt(n+3).

6, 7, 8, 9, 10, 10, 11, 12, 12, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 18, 19, 19, 20, 20, 20, 21, 21, 22, 22, 22, 23, 23, 23, 24, 24, 24, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 28, 28, 28, 28, 29, 29, 29, 30, 30, 30, 30, 31, 31, 31, 31, 32, 32, 32, 32, 33, 33, 33, 33, 34

Offset

1,1

Links

Table of n, a(n) for n=1..71.

X. Zhan, Formulae for sums of consecutive square roots, The Math. Intelligencer, 27, No. 4, 2005, 4-5.

Formula

a(n) = floor(sqrt(16n+20)).

Maple

seq(floor(sqrt(16*n+20)), n=1..90);

Mathematica

Table[Floor[Sqrt[16 n + 20]], {n, 80}] (* Vincenzo Librandi, Jun 28 2015 *)

Prog

(PARI) vector(80, n, sqrtint(16*n+20)) \\ Michel Marcus, Jun 27 2015
(Magma) [Floor(Sqrt(16*n+20)): n in [1..80]]; // Vincenzo Librandi, Jun 28 2015

Crossrefs

Cf. A000267, A114458, A114460.

Sequence in context: A248418 A168679 A102304 * A168096 A030546 A028253

Adjacent sequences: A114456 A114457 A114458 * A114460 A114461 A114462

Keyword

nonn

Author

Emeric Deutsch, Nov 28 2005

Status

approved