A335056 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) is the number of vertices inside the k-th rectangle.

1, 3, 3, 5, 11, 5, 7, 19, 19, 7, 9, 29, 43, 29, 9, 11, 37, 61, 61, 37, 11, 13, 47, 83, 105, 83, 47, 13, 15, 57, 103, 143, 143, 103, 57, 15, 17, 69, 125, 183, 211, 183, 125, 69, 17, 19, 81, 143, 215, 267, 267, 215, 143, 81, 19, 21, 95, 167, 253, 329, 369, 329, 253, 167, 95, 21, 23, 109, 189, 289, 385, 455, 455, 385, 289, 189, 109, 23

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..78.

Scott R. Shannon, Image for n = 2 showing the count of the vertices.

Scott R. Shannon, Image for n = 3 showing the count of the vertices.

Scott R. Shannon, Image for n = 5 showing the count of the vertices.

Scott R. Shannon, Image for n = 9 showing the count of the vertices.

Scott R. Shannon, Image for n = 12 showing the count of the vertices.

Formula

Row sum n + Row sum A335074(n) = A159065(n).

Example

Triangle begins:
1;
3, 3;
5, 11, 5;
7, 19, 19, 7;
9, 29, 43, 29, 9;
11, 37, 61, 61, 37, 11;
13, 47, 83, 105, 83, 47, 13;
15, 57, 103, 143, 143, 103, 57, 15;
17, 69, 125, 183, 211, 183, 125, 69, 17;
19, 81, 143, 215, 267, 267, 215, 143, 81, 19;
21, 95, 167, 253, 329, 369, 329, 253, 167, 95, 21;
23, 109, 189, 289, 385, 455, 455, 385, 289, 189, 109, 23;
25, 125, 215, 331, 451, 551, 597, 551, 451, 331, 215, 125, 25;

Crossrefs

Cf. A335074, A159065, A331755, A333288, A306302.

Sequence in context: A100886 A326175 A072337 * A132751 A218354 A286514

Adjacent sequences: A335053 A335054 A335055 * A335057 A335058 A335059

Keyword

nonn,tabl

Author

Scott R. Shannon and N. J. A. Sloane, May 21 2020

Status

approved