A357061 Number of edges in a square when n internal squares are drawn between the 4n points that divide each side into n+1 equal parts.

4, 12, 36, 76, 132, 180, 292, 348, 516, 604, 804, 892, 1156, 1284, 1572, 1708, 2052, 2180, 2596, 2796, 3204, 3412, 3876, 4012, 4612, 4860, 5412, 5668, 6276, 6508, 7204, 7460, 8172, 8524, 9252, 9516, 10372, 10740, 11532, 11900, 12804, 13100, 14116, 14532, 15468, 15940, 16932, 17196, 18436

Offset: 0

Author

Scott R. Shannon, Sep 10 2022

Keywords

• nonn

Comments

The even values of n that yield squares with non-simple intersections are 32, 38, 44, 50, 54, 62, 76, 90, 98, ... .

See A357058 and A357060 for images of the squares.

Crossrefs

Cf. A357058 (regions), A357060 (vertices), A355948, A355840, A355800, A357008 (triangle).

Formula

a(n) = A357058(n) + A357060(n) - 1 by Euler's formula.

Conjecture: a(n) = 8*n^2 + 4 for squares that only contain simple intersections when cut by n internal squares. This is never the case for odd n >= 5.