A331763 Number of vertices formed by drawing the lines connecting any two of the 2*(n+2) perimeter points of a 3 X (n+1) rectangular grid of points (or equally, a 2 X n grid of squares).

13, 37, 99, 213, 401, 657, 1085, 1619, 2327, 3257, 4457, 5883, 7751, 9885, 12403, 15513, 19131, 23181, 28115, 33601, 39745, 46821, 54865, 63733, 73879, 84889, 97063, 110639, 125649, 141797, 160129, 179981, 201175, 224481, 249403, 276291, 306003, 337425

Offset: 1

Author

Scott R. Shannon and N. J. A. Sloane, Feb 05 2020

Keywords

• nonn

Comments

Triangles A331452, A331453, A331454 do not have formulas, except for column 1. The column 2 sequences, A331763, A331765, A331766, are therefore the next ones to attack.

See A331452 for other illustrations.

Links

• Lars Blomberg, Table of n, a(n) for n = 1..100
• Lars Blomberg, Scott R. Shannon, and N. J. A. Sloane, Graphical Enumeration and Stained Glass Windows, 1: Rectangular Grids, (2020). Also arXiv:2009.07918.
• Scott R. Shannon, Colored illustration for a(3) = 99
• Scott R. Shannon, Data specifically for nX2 (or 2Xn) rectangles
• N. J. A. Sloane (in collaboration with Scott R. Shannon), Art and Sequences, Slides of guest lecture in Math 640, Rutgers Univ., Feb 8, 2020. Mentions this sequence.
• N. J. A. Sloane, "A Handbook of Integer Sequences" Fifty Years Later, arXiv:2301.03149 [math.NT], 2023, p. 20.

Crossrefs

Column 2 of A331453.

Cf. A331765, A331766, A331767.

Extensions

More terms from Scott R. Shannon, Mar 11 2020

a(21) and beyond from Lars Blomberg, Apr 28 2020