login
A370007
Minimum number of curves of length 1 required to form a convex perimeter around n non-overlapping unit circles.
0
0, 7, 11, 13, 15, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33
OFFSET
0,2
COMMENTS
Inspired by the kissing and circle packing problems.
The radius that any unit length must make is 1 and only one bend per unit length.
EXAMPLE
a(0) = 0;
a(1) = 7 = ceiling(2*Pi), a single unit circle has a circumference of 2Pi;
a(2) = 11 = ceiling(2*Pi+4), two adjacent unit circles;
a(3) = 13 = ceiling(2*Pi+6), three coins arranged in a triangle - 2 circles in one row and one circle above;
a(4) = 15 = ceiling(2*Pi+8), four circles arranged in a square or parallelogram;
a(5) = 17 = ceiling(2*Pi+10), for 5 circles, either 3 in one row and two in the other, 2,2,&1 or 5 in a circle;
a(6) = 18 = ceiling(2*pi+8+4*cos(Pi/6)), for 6 circles, see Table 1, C06 and Fig. 7 in Kallrath & Frey;
a(7) = 19 = ceiling(2*Pi+12), for 7, it is 2,3,2 pattern;
a(8) = 21 = ceiling(2*Pi+14);
a(9) = 22 = ceiling(2*Pi+12+4*cos(Pi/6));
a(10) = 23 = ceiling(2*Pi+16);
a(11) = 24 = ceiling(2*Pi+14+4*cos(Pi/6));
a(12) = 25 = ceiling(2*Pi+18);
a(13) = 26 = ceiling(2*Pi+16+4*cos(Pi/6));
a(14) = 27 = ceiling(2*Pi+20);
a(15) = 28 = ceiling(2*Pi+18+4*cos(Pi/6));
a(16) = 29 = ceiling(2*Pi+22);
a(17) = 30 = ceiling(2*Pi+20+4*cos(Pi/6));
a(18) = 31 = ceiling(2*Pi+24);
a(19) = 33 = ceiling(2*Pi+26);
CROSSREFS
Sequence in context: A245178 A287161 A051266 * A172247 A374082 A172120
KEYWORD
nonn,more
AUTHOR
Robert G. Wilson v, Feb 07 2024
STATUS
approved