A245207 a(n) = floor((n + sqrt(2))^2).

2, 5, 11, 19, 29, 41, 54, 70, 88, 108, 130, 154, 179, 207, 237, 269, 303, 339, 376, 416, 458, 502, 548, 596, 645, 697, 751, 807, 865, 925, 986, 1050, 1116, 1184, 1254, 1325, 1399, 1475, 1553, 1633, 1715, 1798, 1884, 1972, 2062, 2154, 2248, 2343, 2441, 2541, 2643, 2747, 2853, 2960, 3070

Offset

0,1

Comments

For n >= 1, a(n) is the curvature (truncated to integer), in increasing order, of circles which are inscribed between a unit circle and a unit square. The basic calculation is based on formula (2) in the "Soddy Circles" article in MathWorld web site. See illustration.

Links

G. C. Greubel, Table of n, a(n) for n = 0..10000

Kival Ngaokrajang, Illustration of initial terms.

Eric Weisstein's World of Mathematics, Soddy Circles.

Formula

a(n) = floor((n + sqrt(2))^2).

Maple

A245207:=n->floor((n + sqrt(2))^2): seq(A245207(n), n=0..50); # Wesley Ivan Hurt, Jul 14 2014

Mathematica

Table[Floor[(n + Sqrt[2])^2], {n, 0, 49}] (* Alonso del Arte, Jul 13 2014 *)

Prog

(PARI) {print1(2, ", "); for (n=1, 100, print1(floor((n+sqrt(2))^2), ", "))}
(Magma) [Floor((n+Sqrt(2))^2): n in [0..50]]; // G. C. Greubel, Sep 30 2018

Crossrefs

Sequence in context: A088796 A190309 A161550 * A215762 A085626 A258031

Adjacent sequences: A245204 A245205 A245206 * A245208 A245209 A245210

Keyword

nonn,easy

Author

Kival Ngaokrajang, Jul 13 2014

Status

approved