A346112 Size of the smallest regular polygon chain for a regular polygon with n sides.

6, 4, 6, 3, 6, 4, 6, 5, 6, 3, 6, 4, 6, 4, 6, 3, 6, 4

Offset

3,1

Comments

Each polygon in a polygon chain shares one edge with both its predecessor and successor polygon. The polygon chain forms a connected cycle.

Links

Table of n, a(n) for n=3..20.

Stuart Anderson, Smallest regular polygon chains for n= 3 to 16

Dan McKinnon, Regular polygons, in rings

Formula

Empirical observations for n >= 3:

a(n) = 3 if n == 0 (mod 6),

4 if n == 4 or 8 (mod 12),

5 if n = 10,

4 if n = 14,

6 otherwise.

Example

For n = 6, 3 hexagons can form a ring.  See the first link for this and further images.

Prog

(C++)
#include <iostream>
using namespace std;
int a(int n);
int main() {
    int t = 30; //change to extend the number of terms
    for (int n = 3; n < t; n++){
        cout<< "n= "<<n<<" a(n)= "<<a(n)<<endl;
    }
    return 0;
}
int a(int n) {
    int s =0;
    if (n%6 == 0) {
        s = 3;
    } else if (n == 10) {
        s = 5;
    } else if (n == 14) {
        s = 4;
    } else if (n%4 == 0) {
        s = 4;
    } else {
        s = 6;
    }
    return s;
}

Crossrefs

Sequence in context: A153606 A086057 A254307 * A176394 A198235 A226294

Adjacent sequences: A346109 A346110 A346111 * A346113 A346114 A346115

Keyword

nonn,more,hear

Author

Stuart E Anderson, Jul 05 2021

Status

approved