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

0,1

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.

Links

Table of n, a(n) for n=0..48.

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.

Crossrefs

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

Sequence in context: A095735 A020875 A307182 * A190072 A063810 A183931

Adjacent sequences: A357058 A357059 A357060 * A357062 A357063 A357064

Keyword

nonn

Author

Scott R. Shannon, Sep 10 2022

Status

approved