A275161 Number of sides of a polygon formed by tiling n squares in a spiral.

4, 4, 6, 4, 6, 4, 6, 6, 4, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6, 6, 6, 4, 6, 6, 6, 6, 6, 6

Offset: 1

Author

Eric Ginsburg, Nov 13 2016

Keywords

• nonn
• easy

Examples

			From _Jon E. Schoenfield_, Nov 20 2016: (Start)
The order in which tiles are added to the spiral follows the numbering in the figure below:
.
  +----+----+----+----+----+
  | 25 | 10 | 11 | 12 | 13 |
  +----+----+----+----+----+
  | 24 |  9 |  2 |  3 | 14 |
  +----+----+----+----+----+
  | 23 |  8 |  1 |  4 | 15 |
  +----+----+----+----+----+
  | 22 |  7 |  6 |  5 | 16 |
  +----+----+----+----+----+
  | 21 | 20 | 19 | 18 | 17 |
  +----+----+----+----+----+
(End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A002620, A240025.

Programs

Mathematica

Table[If[Floor[Floor[Sqrt[4*n + 1]]^2/4] == n, 4, 6], {n, 1, 100}] (* Vaclav Kotesovec, Dec 02 2021 *)

PARI

a(n)=if(sqrtint(4*n+1)^2\4==n, 4, 6) \\ Charles R Greathouse IV, Nov 20 2016

Formula

a(n) = 4 for n in A002620, 6 otherwise. - Jon E. Schoenfield, Nov 19 2016

a(n) = 6 - 2*A240025(n). [See above] - Antti Karttunen, Nov 30 2021