A266685 T(n,k) is the number of loops appearing in pattern of circular arc connecting two vertices of regular polygons. (See Comments.)

1, 2, 1, 1, 2, 1, 4, 1, 1, 2, 3, 2, 1, 6, 1, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 1, 2, 1, 2, 1, 2, 7, 2, 1, 2, 1, 2, 1, 14, 1, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 1, 2, 3, 2, 1, 6, 1, 2, 9, 2, 1, 6, 1, 2, 3, 2, 1, 18

Offset

0,2

Comments

The patterns in A262343 and A264906 can be considered as case of skip 0 and 1 vertex of circle construction on regular polygons. k is the cyclic number of loops of the case skip n-vertices. See illustration for more details.

T(n,k) is conjectured to be even rows of A109004 (excluding the first column).

Links

Table of n, a(n) for n=0..97.

Kival Ngaokrajang, Illustration of initial terms

Formula

T(n,k) = gcd(2*n+3+k, k+1), n >= 0, k = 0..2*n+1.

Example

Irregular triangle begins:
n\k   0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 ...
0     1  2
1     1  2  1  4
2     1  2  3  2  1  6
3     1  2  1  4  1  2  1  8
4     1  2  1  2  5  2  1  2  1 10
5     1  2  3  4  1  6  1  4  3  2  1 12
6     1  2  1  2  1  2  7  2  1  2  1  2  1 14
7     1  2  1  4  1  2  1  8  1  2  1  4  1  2  1 16
...

Mathematica

Table[GCD[2 n + 3 + k, k + 1], {n, 0, 8}, {k, 0, 2 n + 1}] // Flatten (* Michael De Vlieger, Jan 03 2016 *)

Prog

(PARI) for (n=0, 20, for (k=0, 2*n+2, t=gcd(2*n+3+k, k+1); print1(t, ", ")))

Crossrefs

Cf. A109004, A262343, A264906.

Sequence in context: A132066 A102190 A138650 * A272620 A304080 A137843

Adjacent sequences: A266682 A266683 A266684 * A266686 A266687 A266688

Keyword

nonn,tabf

Author

Kival Ngaokrajang, Jan 02 2016

Status

approved