A217573 Number of integers between -(2*n+1)*Pi and (2*n+2)*Pi.

10, 22, 34, 47, 60, 72, 84, 98, 110, 122, 135, 148, 160, 172, 186, 198, 210, 223, 236, 248, 260, 274, 286, 298, 311, 324, 336, 348, 362, 374, 386, 399, 412, 424, 436, 450, 462, 474, 487, 500, 512, 524, 538, 550, 562, 575, 588, 600, 612, 626, 638, 650, 663

Offset

0,1

Comments

a(n) is the number of lattice points inside spiral r=theta and on X-axis counted until the (n+1)-th loop of the spiral.

Links

Table of n, a(n) for n=0..52.

César Eliud Lozada, Plot of spiral

Formula

a(n) = floor((2*n+1)*Pi) + floor((2*n+2)*Pi) + 1.

Maple

A := []:
for n from 0 to 80 do
  n1 := floor((2*n+1)*Pi):
  n2 := floor((2*n+2)*Pi):
  A := [op(A), n1+n2+1]
end do:
A:=A;

Mathematica

Table[Ceiling[Pi(2n+2)]+Floor[Pi(2n+1)], {n, 0, 60}] (* Harvey P. Dale, Aug 25 2014 *)

Crossrefs

Cf. A001951.

Sequence in context: A339003 A017641 A232540 * A276626 A211482 A177791

Adjacent sequences: A217570 A217571 A217572 * A217574 A217575 A217576

Keyword

nonn

Author

César Eliud Lozada, Oct 08 2012

Status

approved