A335074 Triangle read by rows: consider a figure made up of a row of n congruent rectangles and the diagonals of all possible rectangles; T(n,k) (1 <= k <= n-1) is the number of vertices on the edge separating rectangles k and k+1.

1, 3, 3, 5, 3, 5, 7, 7, 7, 7, 9, 9, 7, 9, 9, 11, 13, 11, 11, 13, 11, 13, 15, 17, 11, 17, 15, 13, 15, 19, 19, 19, 19, 19, 19, 15, 17, 21, 25, 21, 19, 21, 25, 21, 17, 19, 25, 29, 29, 23, 23, 29, 29, 25, 19, 21, 27, 33, 33, 33, 23, 33, 33, 33, 27, 21, 23, 31, 37, 39, 39, 35, 35, 39, 39, 37, 31, 23

Offset: 2

Author

Scott R. Shannon and N. J. A. Sloane, May 22 2020

Keywords

• nonn
• tabl

Comments

The terms are from numeric computation - no formula for a(n) is currently known.

Examples

			Triangle begins:
1;
3, 3;
5, 3, 5;
7, 7, 7, 7;
9, 9, 7, 9, 9;
11, 13, 11, 11, 13, 11;
13, 15, 17, 11, 17, 15, 13;
15, 19, 19, 19, 19, 19, 19, 15;
17, 21, 25, 21, 19, 21, 25, 21, 17;
19, 25, 29, 29, 23, 23, 29, 29, 25, 19;
21, 27, 33, 33, 33, 23, 33, 33, 33, 27, 21;
23, 31, 37, 39, 39, 35, 35, 39, 39, 37, 31, 23;
		

Links

• Scott R. Shannon, Image for n = 3 showing the count of the vertices.
• Scott R. Shannon, Image for n = 4 showing the count of the vertices.
• Scott R. Shannon, Image for n = 7 showing the count of the vertices.
• Scott R. Shannon, Image for n = 10 showing the count of the vertices.
• Scott R. Shannon, Image for n = 12 showing the count of the vertices.

Crossrefs

Cf. A335056, A159065, A331755, A333288, A306302.

Formula

Row sum n + Row sum A335056(n) = A159065(n).